Method and apparatus for a primary transform using an 8-bit transform core

ABSTRACT

A method of decoding or encoding including receiving information regarding a video sequence for encoding or decoding, determining, for the encoding or decoding of the video sequence, whether to use a first transform core matrix that is of a first size type or a second transform core matrix that is of a second size type, and based on the determining, transmitting information that causes the video sequence to be encoded or decoded using the determined first transform core matrix or second transform core matrix.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a Continuation application of U.S. application Ser.No. 16/391,935, filed on Apr. 23, 2019, which claims priority from U.S.Provisional Patent Application No. 62/704,036, filed on Dec. 6, 2018, inthe United States Patent and Trademark Office, the disclosures of whichare incorporated in their entireties.

BACKGROUND 1. Field

Methods and apparatuses consistent with embodiments relate to videocoding, and more particularly, a method and an apparatus for a primarytransform using an 8-bit transform core. The transform core matrices ofsmaller DCT-2 are part of larger DCT-2.

2. Description of Related Art

In HEVC, primary transforms may be 4-point, 8-point, 16-point and32-point DCT-2, and the transform core matrices are represented using8-bit integers, i.e., 8-bit transform core.

SUMMARY

According to embodiments, a method of decoding or encoding is performedby at least one processor and includes receiving information regarding avideo sequence for encoding or decoding; determining, for the encodingor decoding of the video sequence, whether to use a first transform corematrix that is of a first size type or a second transform core matrixthat is of a second size type; and based on the determining,transmitting information that causes the video sequence to be encoded ordecoded using the determined first transform core matrix or secondtransform core matrix.

According to embodiments, an apparatus for decoding or encoding of avideo sequence includes at least one memory configured to store computerprogram code, and at least one processor configured to access the atleast one memory and operate according to the computer program code. Thecomputer program code includes receiving code configured to cause the atleast one processor to receive information regarding a video sequencefor encoding or decoding. The computer program code further includesdetermining code configured to cause the at least one processor todetermine, for the encoding or decoding of the video sequence, whetherto use a first transform core matrix that is of a first size type or asecond transform core matrix that is of a second size type. The computerprogram code further includes transmitting code configured to cause theat least one processor to, based on the determining, transmitinformation that causes the video sequence to be encoded or decodedusing the determined first transform core matrix or second transformcore matrix.

According to embodiments, a non-transitory computer-readable storagemedium stores instructions that cause at least one processor to receiveinformation regarding a video sequence for encoding or decoding. Theinstructions further cause the at least one processor to determine, forthe encoding or decoding of the video sequence, whether to use a firsttransform core matrix that is of a first size type or a second transformcore matrix that is of a second size type. The instructions furthercause the at least one processor to, based on the determining, transmitinformation that causes the video sequence to be encoded or decodedusing the determined first transform core matrix or second transformcore matrix

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A to 1D are diagrams illustrating example transform corematrices.

FIG. 2 is a simplified block diagram of a communication system accordingto an embodiment.

FIG. 3 is a diagram of a placement of a video encoder and a videodecoder in a streaming environment, according to an embodiment.

FIG. 4 is a functional block diagram of a video decoder according to anembodiment.

FIG. 5 is a functional block diagram of a video encoder according to anembodiment.

FIG. 6 is a flowchart illustrating a method of decoding or encoding of avideo sequence, according to an embodiment.

FIG. 7 is a diagram illustrating example transform core matrices,according to an embodiment.

FIG. 8 is a simplified block diagram of an apparatus for decoding orencoding of a video sequence, according to an embodiment.

FIG. 9 is a diagram of a computer system suitable for implementingembodiments.

DETAILED DESCRIPTION

In HEVC, the primary transforms are 4-point, 8-point, 16-point and32-point DCT-2, and the transform core matrices are represented using8-bit integers, i.e., 8-bit transform core. The transform core matricesof smaller DCT-2 are part of larger DCT-2, as illustrated in FIGS. 1A to1D. FIG. 1A illustrates a 4×4 transform. FIG. 1B illustrates an 8×8transform. FIG. 1C illustrates a 16×16 transform. FIG. 1D illustrates a32×32 transform.

As illustrated in FIGS. 1A to 1D, the DCT-2 cores showsymmetry/anti-symmetry characteristics, thus a so-called “partialbutterfly” implementation is supported to reduce the number of operationcounts (multiplications, adds/subs, shifts), and identical results ofmatrix multiplication can be obtained using partial butterfly.

In VVC, besides 4-point, 8-point, 16-point and 32-point DCT-2 transformswhich are the same as HEVC, additional 2-point and 64-point DCT-2 mayalso be included.

The 64-point DCT-2 core defined in VVC is shown below as a 64×64 matrix:

{  { aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa }  { bf, bg, bh, bi, bj, bk,bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc,cd, ce, cf, cg, ch, ci, cj, ck, −ck, −cj, −ci, −ch, −cg, −cf, −ce, −cd,−cc, −cb, −ca, −bz, −by, −bx, −bw, −bv, −bu, −bt, −bs, −br, −bq, −bp,−bo, −bn, −bm, −bl, −bk, −bj, −bi, −bh, −bg, −bf }  { ap, aq, ar, as,at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, −be, −bd, −bc, −bb, −ba,−az, −ay, −ax, −aw, −av, −au, −at, −as, −ar, −aq, −ap, −ap, −aq, −ar,−as, −at, −au, −av, −aw, −ax, −ay, −az, −ba, −bb, −bc, −bd, −be, be, bd,bc, bb, ba, az, ay, ax, aw, av, au, at, as, ar, aq, ap }  { bg, bj, bm,bp, bs, bv, by, cb, ce, ch, ck, −ci, −cf, −cc, −bz, −bw, −bt, −bq, −bn,−bk, −bh, −bf, −bi, −bl, −bo, −br, −bu, −bx, −ca, −cd, −cg, −cj, cj, cg,cd, ca, bx, bu, br, bo, bl, bi, bf, bh, bk, bn, bq, bt, bw, bz, cc, cf,ci, −ck, −ch, −ce, −cb, −by, −bv, −bs, −bp, −bm, −bj, −bg }  { ah, ai,aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak, −aj, −ai, −ah, −ah,−ai, −aj, −ak, −al, −am, −an, −ao, ao, an, am, al, ak, aj, ai, ah, ah,ai, aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak, −aj, −ai, −ah, −ah,−ai, −aj, −ak, −al, −am, −an, −ao, ao, an, am, al, ak, aj, ai, ah }  {bh, bm, br, bw, cb, cg, −ck, −cf, −ca, −bv, −bq, −bl, −bg, −bi, −bn,−bs, −bx, −cc, −ch, cj, ce, bz, bu, bp, bk, bf, bj, bo, bt, by, cd, ci,−ci, −cd, −by, −bt, −bo, −bj, −bf, −bk, −bp, −bu, −bz, −ce, −cj, ch, cc,bx, bs, bn, bi, bg, bl, bq, bv, ca, cf, ck, −cg, −cb, −bw, −br, −bm, −bh}  { aq, at, aw, az, bc, −be, −bb, −ay, −av, −as, −ap, −ar, −au, −ax,−ba, −bd, bd, ba, ax, au, ar, ap, as, av, ay, bb, be, −bc, −az, −aw,−at, −aq, −aq, −at, −aw, −az, −bc, be, bb, ay, av, as, ap, ar, au, ax,ba, bd, −bd, −ba, −ax, −au, −ar, −ap, −as, −av, −ay, −bb, −be, bc, az,aw, at, aq }  { bi, bp, bw, cd, ck, −ce, −bx, −bq, −bj, −bh, −bo, −bv,−cc, −cj, cf, by, br, bk, bg, bn, bu, cb, ci, −cg, −bz, −bs, −bl, −bf,−bm, −bt, −ca, −ch, ch, ca, bt, bm, bf, bl, bs, bz, cg, −ci, −cb, −bu,−bn, −bg, −bk, −br, −by, −cf, cj, cc, bv, bo, bh, bj, bq, bx, ce, −ck,−cd, −bw, −bp, −bi }  { ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad }  { bj, bs, cb, ck, −cc, −bt, −bk, −bi, −br,−ca, −cj, cd, bu, bl, bh, bq, bz, ci, −ce, −bv, −bm, −bg, −bp, −by, −ch,cf, bw, bn, bf, bo, bx, cg, −cg, −bx, −bo, −bf, −bn, −bw, −cf, ch, by,bp, bg, bm, bv, ce, −ci, −bz, −bq, −bh, −bl, −bu, −cd, cj, ca, br, bi,bk, bt, cc, −ck, −cb, −bs, −bj }  { ar, aw, bb, −bd, −ay, −at, −ap, −au,−az, −be, ba, av, aq, as, ax, bc, −bc, −ax, −as, −aq, −av, −ba, be, az,au, ap, at, ay, bd, −bb, −aw, −ar, −ar, −aw, −bb, bd, ay, at, ap, au,az, be, −ba, −av, −aq, −as, −ax, −bc, bc, ax, as, aq, av, ba, −be, −az,−au, −ap, −at, −ay, −bd, bb, aw, ar }  { bk, bv, cg, −ce, −bt, −bi, −bm,−bx, −ci, cc, br, bg, bo, bz, ck, −ca, −bp, −bf, −bq, −cb, cj, by, bn,bh, bs, cd, −ch, −bw, −bl, −bj, −bu, −cf, cf, bu, bj, bl, bw, ch, −cd,−bs, −bh, −bn, −by, −cj, cb, bq, bf, bp, ca, −ck, −bz, −bo, −bg, −br,−cc, ci, bx, bm, bi, bt, ce, −cg, −bv, −bk }  { ai, al, ao, −am, −aj,−ah, −ak, −an, an, ak, ah, aj, am, −ao, −al, −ai, −ai, −al, −ao, am, aj,ah, ak, an, −an, −ak, −ah, −aj, −am, ao, al, ai, ai, al, ao, −am, −aj,−ah, −ak, −an, an, ak, ah, aj, am, −ao, −al, −ai, −ai, −al, −ao, am, aj,ah, ak, an, −an, −ak, −ah, −aj, −am, ao, al, ai }  { bl, by, −ck, −bx,−bk, −bm, −bz, cj, bw, bj, bn, ca, −ci, −bv, −bi, −bo, −cb, ch, bu, bh,bp, cc, −cg, −bt, −bg, −bq, −cd, cf, bs, bf, br, ce, −ce, −br, −bf, −bs,−cf, cd, bq, bg, bt, cg, −cc, −bp, −bh, −bu, −ch, cb, bo, bi, bv, ci,−ca, −bn, −bj, −bw, −cj, bz, bm, bk, bx, ck, −by, −bl }  { as, az, −bd,−aw, −ap, −av, −bc, ba, at, ar, ay, −be, −ax, −aq, −au, −bb, bb, au, aq,ax, be, −ay, −ar, −at, −ba, bc, av, ap, aw, bd, −az, −as, −as, −az, bd,aw, ap, av, bc, −ba, −at, −ar, −ay, be, ax, aq, au, bb, −bb, −au, −aq,−ax, −be, ay, ar, at, ba, −bc, −av, −ap, −aw, −bd, az, as }  { bm, cb,−cf, −bq, −bi, −bx, cj, bu, bf, bt, ci, −by, −bj, −bp, −ce, cc, bn, bl,ca, −cg, −br, −bh, −bw, ck, bv, bg, bs, ch, −bz, −bk, −bo, −cd, cd, bo,bk, bz, −ch, −bs, −bg, −bv, −ck, bw, bh, br, cg, −ca, −bl, −bn, −cc, ce,bp, bj, by, −ci, −bt, −bf, −bu, −cj, bx, bi, bq, cf, −cb, −bm }  { ab,ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab,ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab,ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab,ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab }  {bn, ce, −ca, −bj, −br, −ci, bw, bf, bv, −cj, −bs, −bi, −bz, cf, bo, bm,cd, −cb, −bk, −bq, −ch, bx, bg, bu, −ck, −bt, −bh, −by, cg, bp, bl, cc,−cc, −bl, −bp, −cg, by, bh, bt, ck, −bu, −bg, −bx, ch, bq, bk, cb, −cd,−bm, −bo, −cf, bz, bi, bs, cj, −bv, −bf, −bw, ci, br, bj, ca, −ce, −bn } { at, bc, −ay, −ap, −ax, bd, au, as, bb, −az, −aq, −aw, be, av, ar, ba,−ba, −ar, −av, −be, aw, aq, az, −bb, −as, −au, −bd, ax, ap, ay, −bc,−at, −at, −bc, ay, ap, ax, −bd, −au, −as, −bb, az, aq, aw, −be, −av,−ar, −ba, ba, ar, av, be, −aw, −aq, −az, bb, as, au, bd, −ax, −ap, −ay,bc, at }  { bo, ch, −bv, −bh, −ca, cc, bj, bt, −cj, −bq, −bm, −cf, bx,bf, by, −ce, −bl, −br, −ck, bs, bk, cd, −bz, −bg, −bw, cg, bn, bp, ci,−bu, −bi, −cb, cb, bi, bu, −ci, −bp, −bn, −cg, bw, bg, bz, −cd, −bk,−bs, ck, br, bl, ce, −by, −bf, −bx, cf, bm, bq, cj, −bt, −bj, −cc, ca,bh, bv, −ch, −bo }  { aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al,an, ai, ak, −ao, −aj, −aj, −ao, ak, ai, an, −al, −ah, −am, am, ah, al,−an, −ai, −ak, ao, aj, aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al,an, ai, ak, −ao, −aj, −aj, −ao, ak, ai, an, −al, −ah, −am, am, ah, al,−an, −ai, −ak, ao, aj }  { bp, ck, −bq, −bo, −cj, br, bn, ci, −bs, −bm,−ch, bt, bl, cg, −bu, −bk, −cf, bv, bj, ce, −bw, −bi, −cd, bx, bh, cc,−by, −bg, −cb, bz, bf, ca, −ca, −bf, −bz, cb, bg, by, −cc, −bh, −bx, cd,bi, bw, −ce, −bj, −bv, cf, bk, bu, −cg, −bl, −bt, ch, bm, bs, −ci, −bn,−br, cj, bo, bq, −ck, −bp }  { au, −be, −at, −av, bd, as, aw, −bc, −ar,−ax, bb, aq, ay, −ba, −ap, −az, −az, ap, ba, −ay, −aq, −bb, ax, ar, bc,−aw, −as, −bd, av, at, be, −au, −au, be, at, av, −bd, −as, −aw, bc, ar,ax, −bb, −aq, −ay, ba, ap, az, −az, −ap, −ba, ay, aq, bb, −ax, −ar, −bc,aw, as, bd, −av, −at, −be, au }  { bq, −ci, −bl, −bv, cd, bg, ca, −by,−bi, −cf, bt, bn, ck, −bo, −bs, cg, bj, bx, −cb, −bf, −cc, bw, bk, ch,−br, −bp, cj, bm, bu, −ce, −bh, −bz, bz, bh, ce, −bu, −bm, −cj, bp, br,−ch, −bk, −bw, cc, bf, cb, −bx, −bj, −cg, bs, bo, −ck, −bn, −bt, cf, bi,by, −ca, −bg, −cd, bv, bl, ci, −bq }  { ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae }  { br, −cf, −bg, −cc, bu, bo,−ci, −bj, −bz, bx, bl, ck, −bm, −bw, ca, bi, ch, −bp, −bt, cd, bf, ce,−bs, −bq, cg, bh, cb, −bv, −bn, cj, bk, by, −by, −bk, −cj, bn, bv, −cb,−bh, −cg, bq, bs, −ce, −bf, −cd, bt, bp, −ch, −bi, −ca, bw, bm, −ck,−bl, −bx, bz, bj, ci, −bo, −bu, cc, bg, cf, −br }  { av, −bb, −ap, −bc,au, aw, −ba, −aq, −bd, at, ax, −az, −ar, −be, as, ay, −ay, −as, be, ar,az, −ax, −at, bd, aq, ba, −aw, −au, bc, ap, bb, −av, −av, bb, ap, bc,−au, −aw, ba, aq, bd, −at, −ax, az, ar, be, −as, −ay, ay, as, −be, −ar,−az, ax, at, −bd, −aq, −ba, aw, au, −bc, −ap, −bb, av }  { bs, −cc, −bi,−cj, bl, bz, −bv, −bp, cf, bf, cg, −bo, −bw, by, bm, −ci, −bh, −cd, br,bt, −cb, −bj, −ck, bk, ca, −bu, −bq, ce, bg, ch, −bn, −bx, bx, bn, −ch,−bg, −ce, bq, bu, −ca, −bk, ck, bj, cb, −bt, −br, cd, bh, ci, −bm, −by,bw, bo, −cg, −bf, −cf, bp, bv, −bz, −bl, cj, bi, cc, −bs }  { ak, −am,−ai, ao, ah, an, −aj, −al, al, aj, −an, −ah, −ao, ai, am, −ak, −ak, am,ai, −ao, −ah, −an, aj, al, −al, −aj, an, ah, ao, −ai, −am, ak, ak, −am,−ai, ao, ah, an, −aj, −al, al, aj, −an, −ah, −ao, ai, am, −ak, −ak, am,ai, −ao, −ah, −an, aj, al, −al, −aj, an, ah, ao, −ai, −am, ak }  { bt,−bz, −bn, cf, bh, ck, −bi, −ce, bo, by, −bu, −bs, ca, bm, −cg, −bg, −cj,bj, cd, −bp, −bx, bv, br, −cb, −bl, ch, bf, ci, −bk, −cc, bq, bw, −bw,−bq, cc, bk, −ci, −bf, −ch, bl, cb, −br, −bv, bx, bp, −cd, −bj, cj, bg,cg, −bm, −ca, bs, bu, −by, −bo, ce, bi, −ck, −bh, −cf, bn, bz, −bt }  {aw, −ay, −au, ba, as, −bc, −aq, be, ap, bd, −ar, −bb, at, az, −av, −ax,ax, av, −az, −at, bb, ar, −bd, −ap, −be, aq, bc, −as, −ba, au, ay, −aw,−aw, ay, au, −ba, −as, bc, aq, −be, −ap, −bd, ar, bb, −at, −az, av, ax,−ax, −av, az, at, −bb, −ar, bd, ap, be, −aq, −bc, as, ba, −au, −ay, aw } { bu, −bw, −bs, by, bq, −ca, −bo, cc, bm, −ce, −bk, cg, bi, −ci, −bg,ck, bf, cj, −bh, −ch, bj, cf, −bl, −cd, bn, cb, −bp, −bz, br, bx, −bt,−bv, bv, bt, −bx, −br, bz, bp, −cb, −bn, cd, bl, −cf, −bj, ch, bh, −cj,−bf, −ck, bg, ci, −bi, −cg, bk, ce, −bm, −cc, bo, ca, −bq, −by, bs, bw,−bu }  { aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa,−aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa,−aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa,−aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa,−aa, aa }  { bv, −bt, −bx, br, bz, −bp, −cb, bn, cd, −bl, −cf, bj, ch,−bh, −cj, bf, −ck, −bg, ci, bi, −cg, −bk, ce, bm, −cc, −bo, ca, bq, −by,−bs, bw, bu, −bu, −bw, bs, by, −bq, −ca, bo, cc, −bm, −ce, bk, cg, −bi,−ci, bg, ck, −bf, cj, bh, −ch, −bj, cf, bl, −cd, −bn, cb, bp, −bz, −br,bx, bt, −bv }  { ax, −av, −az, at, bb, −ar, −bd, ap, −be, −aq, bc, as,−ba, −au, ay, aw, −aw, −ay, au, ba, −as, −bc, aq, be, −ap, bd, ar, −bb,−at, az, av, −ax, −ax, av, az, −at, −bb, ar, bd, −ap, be, aq, −bc, −as,ba, au, −ay, −aw, aw, ay, −au, −ba, as, bc, −aq, −be, ap, −bd, −ar, bb,at, −az, −av, ax }  { bw, −bq, −cc, bk, ci, −bf, ch, bl, −cb, −br, bv,bx, −bp, −cd, bj, cj, −bg, cg, bm, −ca, −bs, bu, by, −bo, −ce, bi, ck,−bh, cf, bn, −bz, −bt, bt, bz, −bn, −cf, bh, −ck, −bi, ce, bo, −by, −bu,bs, ca, −bm, −cg, bg, −cj, −bj, cd, bp, −bx, −bv, br, cb, −bl, −ch, bf,−ci, −bk, cc, bq, −bw }  { al, −aj, −an, ah, −ao, −ai, am, ak, −ak, −am,ai, ao, −ah, an, aj, −al, −al, aj, an, −ah, ao, ai, −am, −ak, ak, am,−ai, −ao, ah, −an, −aj, al, al, −aj, −an, ah, −ao, −ai, am, ak, −ak,−am, ai, ao, −ah, an, aj, −al, −al, aj, an, −ah, ao, ai, −am, −ak, ak,am, −ai, −ao, ah, −an, −aj, al }  { bx, −bn, −ch, bg, −ce, −bq, bu, ca,−bk, −ck, bj, −cb, −bt, br, cd, −bh, ci, bm, −by, −bw, bo, cg, −bf, cf,bp, −bv, −bz, bl, cj, −bi, cc, bs, −bs, −cc, bi, −cj, −bl, bz, bv, −bp,−cf, bf, −cg, −bo, bw, by, −bm, −ci, bh, −cd, −br, bt, cb, −bj, ck, bk,−ca, −bu, bq, ce, −bg, ch, bn, −bx }  { ay, −as, −be, ar, −az, −ax, at,bd, −aq, ba, aw, −au, −bc, ap, −bb, −av, av, bb, −ap, bc, au, −aw, −ba,aq, −bd, −at, ax, az, −ar, be, as, −ay, −ay, as, be, −ar, az, ax, −at,−bd, aq, −ba, −aw, au, bc, −ap, bb, av, −av, −bb, ap, −bc, −au, aw, ba,−aq, bd, at, −ax, −az, ar, −be, −as, ay }  { by, −bk, cj, bn, −bv, −cb,bh, −cg, −bq, bs, ce, −bf, cd, bt, −bp, −ch, bi, −ca, −bw, bm, ck, −bl,bx, bz, −bj, ci, bo, −bu, −cc, bg, −cf, −br, br, cf, −bg, cc, bu, −bo,−ci, bj, −bz, −bx, bl, −ck, −bm, bw, ca, −bi, ch, bp, −bt, −cd, bf, −ce,−bs, bq, cg, −bh, cb, bv, −bn, −cj, bk, −by }  { af, −ad, ag, ae, −ae,−ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae,−ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae,−ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae,−ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af }  { bz, −bh, ce, bu,−bm, cj, bp, −br, −ch, bk, −bw, −cc, bf, −cb, −bx, bj, −cg, −bs, bo, ck,−bn, bt, cf, −bi, by, ca, −bg, cd, bv, −bl, ci, bq, −bq, −ci, bl, −bv,−cd, bg, −ca, −by, bi, −cf, −bt, bn, −ck, −bo, bs, cg, −bj, bx, cb, −bf,cc, bw, −bk, ch, br, −bp, −cj, bm, −bu, −ce, bh, −bz }  { az, −ap, ba,ay, −aq, bb, ax, −ar, bc, aw, −as, bd, av, −at, be, au, −au, −be, at,−av, −bd, as, −aw, −bc, ar, −ax, −bb, aq, −ay, −ba, ap, −az, −az, ap,−ba, −ay, aq, −bb, −ax, ar, −bc, −aw, as, −bd, −av, at, −be, −au, au,be, −at, av, bd, −as, aw, bc, −ar, ax, bb, −aq, ay, ba, −ap, az }  { ca,−bf, bz, cb, −bg, by, cc, −bh, bx, cd, −bi, bw, ce, −bj, bv, cf, −bk,bu, cg, −bl, bt, ch, −bm, bs, ci, −bn, br, cj, −bo, bq, ck, −bp, bp,−ck, −bq, bo, −cj, −br, bn, −ci, −bs, bm, −ch, −bt, bl, −cg, −bu, bk,−cf, −bv, bj, −ce, −bw, bi, −cd, −bx, bh, −cc, −by, bg, −cb, −bz, bf,−ca }  { am, −ah, al, an, −ai, ak, ao, −aj, aj, −ao, −ak, ai, −an, −al,ah, −am, −am, ah, −al, −an, ai, −ak, −ao, aj, −aj, ao, ak, −ai, an, al,−ah, am, am, −ah, al, an, −ai, ak, ao, −aj, aj, −ao, −ak, ai, −an, −al,ah, −am, −am, ah, −al, −an, ai, −ak, −ao, aj, −aj, ao, ak, −ai, an, al,−ah, am }  { cb, −bi, bu, ci, −bp, bn, −cg, −bw, bg, −bz, −cd, bk, −bs,−ck, br, −bl, ce, by, −bf, bx, cf, −bm, bq, −cj, −bt, bj, −cc, −ca, bh,−bv, −ch, bo, −bo, ch, bv, −bh, ca, cc, −bj, bt, cj, −bq, bm, −cf, −bx,bf, −by, −ce, bl, −br, ck, bs, −bk, cd, bz, −bg, bw, cg, −bn, bp, −ci,−bu, bi, −cb }  { ba, −ar, av, −be, −aw, aq, −az, −bb, as, −au, bd, ax,−ap, ay, bc, −at, at, −bc, −ay, ap, −ax, −bd, au, −as, bb, az, −aq, aw,be, −av, ar, −ba, −ba, ar, −av, be, aw, −aq, az, bb, −as, au, −bd, −ax,ap, −ay, −bc, at, −at, bc, ay, −ap, ax, bd, −au, as, −bb, −az, aq, −aw,−be, av, −ar, ba }  { cc, −bl, bp, −cg, −by, bh, −bt, ck, bu, −bg, bx,ch, −bq, bk, −cb, −cd, bm, −bo, cf, bz, −bi, bs, −cj, −bv, bf, −bw, −ci,br, −bj, ca, ce, −bn, bn, −ce, −ca, bj, −br, ci, bw, −bf, bv, cj, −bs,bi, −bz, −cf, bo, −bm, cd, cb, −bk, bq, −ch, −bx, bg, −bu, −ck, bt, −bh,by, cg, −bp, bl, −cc }  { ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab,ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab,ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab,ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab,ab, −ac, −ac, ab, −ab, ac }  { cd, −bo, bk, −bz, −ch, bs, −bg, bv, −ck,−bw, bh, −br, cg, ca, −bl, bn, −cc, −ce, bp, −bj, by, ci, −bt, bf, −bu,cj, bx, −bi, bq, −cf, −cb, bm, −bm, cb, cf, −bq, bi, −bx, −cj, bu, −bf,bt, −ci, −by, bj, −bp, ce, cc, −bn, bl, −ca, −cg, br, −bh, bw, ck, −bv,bg, −bs, ch, bz, −bk, bo, −cd }  { bb, −au, aq, −ax, be, ay, −ar, at,−ba, −bc, av, −ap, aw, −bd, −az, as, −as, az, bd, −aw, ap, −av, bc, ba,−at, ar, −ay, −be, ax, −aq, au, −bb, −bb, au, −aq, ax, −be, −ay, ar,−at, ba, bc, −av, ap, −aw, bd, az, −as, as, −az, −bd, aw, −ap, av, −bc,−ba, at, −ar, ay, be, −ax, aq, −au, bb }  { ce, −br, bf, −bs, cf, cd,−bq, bg, −bt, cg, cc, −bp, bh, −bu, ch, cb, −bo, bi, −bv, ci, ca, −bn,bj, −bw, cj, bz, −bm, bk, −bx, ck, by, −bl, bl, −by, −ck, bx, −bk, bm,−bz, −cj, bw, −bj, bn, −ca, −ci, bv, −bi, bo, −cb, −ch, bu, −bh, bp,−cc, −cg, bt, −bg, bq, −cd, −cf, bs, −bf, br, −ce }  { an, −ak, ah, −aj,am, ao, −al, ai, −ai, al, −ao, −am, aj, −ah, ak, −an, −an, ak, −ah, aj,−am, −ao, al, −ai, ai, −al, ao, am, −aj, ah, −ak, an, an, −ak, ah, −aj,am, ao, −al, ai, −ai, al, −ao, −am, aj, −ah, ak, −an, −an, ak, −ah, aj,−am, −ao, al, −ai, ai, −al, ao, am, −aj, ah, −ak, an }  { cf, −bu, bj,−bl, bw, −ch, −cd, bs, −bh, bn, −by, cj, cb, −bq, bf, −bp, ca, ck, −bz,bo, −bg, br, −cc, −ci, bx, −bm, bi, −bt, ce, cg, −bv, bk, −bk, bv, −cg,−ce, bt, −bi, bm, −bx, ci, cc, −br, bg, −bo, bz, −ck, −ca, bp, −bf, bq,−cb, −cj, by, −bn, bh, −bs, cd, ch, −bw, bl, −bj, bu, −cf }  { bc, −ax,as, −aq, av, −ba, −be, az, −au, ap, −at, ay, −bd, −bb, aw, −ar, ar, −aw,bb, bd, −ay, at, −ap, au, −az, be, ba, −av, aq, −as, ax, −bc, −bc, ax,−as, aq, −av, ba, be, −az, au, −ap, at, −ay, bd, bb, −aw, ar, −ar, aw,−bb, −bd, ay, −at, ap, −au, az, −be, −ba, av, −aq, as, −ax, bc }  { cg,−bx, bo, −bf, bn, −bw, cf, ch, −by, bp, −bg, bm, −bv, ce, ci, −bz, bq,−bh, bl, −bu, cd, cj, −ca, br, −bi, bk, −bt, cc, ck, −cb, bs, −bj, bj,−bs, cb, −ck, −cc, bt, −bk, bi, −br, ca, −cj, −cd, bu, −bl, bh, −bq, bz,−ci, −ce, bv, −bm, bg, −bp, by, −ch, −cf, bw, −bn, bf, −bo, bx, −cg }  {ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag,ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag,ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag,ag, −af, ae, −ad, ad, −ae, af, −ag, −ag, af, −ae, ad, −ad, ae, −af, ag } { ch, −ca, bt, −bm, bf, −bl, bs, −bz, cg, ci, −cb, bu, −bn, bg, −bk,br, −by, cf, cj, −cc, bv, −bo, bh, −bj, bq, −bx, ce, ck, −cd, bw, −bp,bi, −bi, bp, −bw, cd, −ck, −ce, bx, −bq, bj, −bh, bo, −bv, cc, −cj, −cf,by, −br, bk, −bg, bn, −bu, cb, −ci, −cg, bz, −bs, bl, −bf, bm, −bt, ca,−ch }  { bd, −ba, ax, −au, ar, −ap, as, −av, ay, −bb, be, bc, −az, aw,−at, aq, −aq, at, −aw, az, −bc, −be, bb, −ay, av, −as, ap, −ar, au, −ax,ba, −bd, −bd, ba, −ax, au, −ar, ap, −as, av, −ay, bb, −be, −bc, az, −aw,at, −aq, aq, −at, aw, −az, bc, be, −bb, ay, −av, as, −ap, ar, −au, ax,−ba, bd }  { ci, −cd, by, −bt, bo, −bj, bf, −bk, bp, −bu, bz, −ce, cj,ch, −cc, bx, −bs, bn, −bi, bg, −bl, bq, −bv, ca, −cf, ck, cg, −cb, bw,−br, bm, −bh, bh, −bm, br, −bw, cb, −cg, −ck, cf, −ca, bv, −bq, bl, −bg,bi, −bn, bs, −bx, cc, −ch, −cj, ce, −bz, bu, −bp, bk, −bf, bj, −bo, bt,−by, cd, −ci }  { ao, −an, am, −al, ak, −aj, ai, −ah, ah, −ai, aj, −ak,al, −am, an, −ao, −ao, an, −am, al, −ak, aj, −ai, ah, −ah, ai, −aj, ak,−al, am, −an, ao, ao, −an, am, −al, ak, −aj, ai, −ah, ah, −ai, aj, −ak,al, −am, an, −ao, −ao, an, −am, al, −ak, aj, −ai, ah, −ah, ai, −aj, ak,−al, am, −an, ao }  { ci, −cg, cd, −ca, bx, −bu, br, −bo, bl, −bi, bf,−bh, bk, −bn, bq, −bt, bw, −bz, cc, −cf, ci, ck, −ch, ce, −cb, by, −bv,bs, −bp, bm, −bj, bg, −bg, bj, −bm, bp, −bs, bv, −by, cb, −ce, ch, −ck,−ci, cf, −cc, bz, −bw, bt, −bq, bn, −bk, bh, −bf, bi, −bl, bo, −br, bu,−bx, ca, −cd, cg, −cj }  { be, −bd, bc, −bb, ba, −az, ay, −ax, aw, −av,au, −at, as, −ar, aq, −ap, ap, −aq, ar, −as, at, −au, av, −aw, ax, −ay,az, −ba, bb, −bc, bd, −be, −be, bd, −bc, bb, −ba, az, −ay, ax, −aw, av,−au, at, −as, ar, −aq, ap, −ap, aq, −ar, as, −at, au, −av, aw, −ax, ay,−az, ba, −bb, bc, −bd, be }  { ck, −cj, ci, −ch, cg, −cf, ce, −cd, cc,−cb, ca, −bz, by, −bx, bw, −bv, bu, −bt, bs, −br, bq, −bp, bo, −bn, bm,−bl, bk, −bj, bi, −bh, bg, −bf, bf, −bg, bh, −bi, bj, −bk, bl, −bm, bn,−bo, bp, −bq, br, −bs, bt, −bu, bv, −bw, bx, −by, bz, −ca, cb, −cc, cd,−ce, cf, −cg, ch, −ci, cj, −ck } } where { aa, ab, ac, ad, ae, af, ag,ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax, ay,az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq,br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci,cj, ck } = {64, 83, 36, 89, 75, 50, 18, 90, 87, 80, 70, 57, 43, 25, 9,90, 90, 88, 85, 82, 78, 73, 67, 61, 54, 46, 38, 31, 22, 13, 4, 91, 90,90, 90, 88, 87, 86, 84, 83, 81, 79, 77, 73, 71, 69, 65, 62, 59, 56, 52,48, 44, 41, 37, 33, 28, 24, 20, 15, 11, 7, 2}

In addition to DCT-2 and 4×4 DST-7 which have been employed in HEVC, anAdaptive Multiple Transform (AMT, also known as Enhanced MultipleTransform (EMT), or known as Multiple Transform Selection (MTS)) schemehas been used in VVC for residual coding for both inter and intra codedblocks. It uses multiple selected transforms from the DCT/DST familiesother than the current transforms in HEVC. The newly introducedtransform matrices are DST-7, DCT-8. Table 1 shows the basis functionsof the selected DST/DCT.

TABLE 1 Transform basis functions of DCT-2, DST-7 and DCT-8 for N-pointinput Transform Type Basis function T_(i)(j), i, j = 0, 1, . . . , N − 1DCT-2 $\quad\begin{matrix}{{T_{i}(j)} = {{\omega_{0} \cdot \sqrt{\frac{2}{N}} \cdot \cos}\mspace{11mu}\left( \frac{\pi \cdot i \cdot \left( {{2j} + 1} \right)}{2N} \right)}} \\{{{where}\mspace{14mu}\omega_{0}} = \left\{ \begin{matrix}\sqrt{\frac{2}{N}} & {i = 0} \\1 & {i \neq 0}\end{matrix} \right.}\end{matrix}$ DCT-8${T_{i}(j)} = {{\sqrt{\frac{4}{{2N} + 1}} \cdot \cos}\mspace{11mu}\left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {{2j} + 1} \right)}{{4N} + 2} \right)}$DST-7${T_{i}(j)} = {{\sqrt{\frac{4}{{2N} + 1}} \cdot \sin}\mspace{11mu}\left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {j + 1} \right)}{{2N} + 1} \right)}$

All the primary transform matrices in VVC are used with 8-bitrepresentation. The AMT applies to the CUs with both width and heightsmaller than or equal to 32, and whether AMT applies or not iscontrolled by a flag called mts_flag. When the mts_flag is equal to 0,only DCT-2 is applied for coding the residue. When the mts_flag is equalto 1, an index mts_idx is further signalled using 2 bins to identify thehorizontal and vertical transform to be used according Table 2, wherevalue 1 means using DST-7 and value 2 means using DCT-8.

TABLE 2 Specification of trTypeHor and trTypeVer depending on mts_idx[ x][ y ][ cIdx ] mts_idx[xTbY ][ yTbY ][ cIdx ] trTypeHor trTypeVer −1 0 00 1 1 1 2 1 2 1 2 3 2 2

The transform core, which is a matrix composed by the basis vectors, ofDST-7 can be represented as below:

4-point DST-7:

{ a,  b,  c,  d } { c,  c,  0, −c } { d, −a, −c,  b } { b, −d,  c, −a }where {a, b, c, d}={29, 55, 74, 84}8-point DST-7:

{ a,  b,  c,  d,  e,  f,  g,  h, } { c,  f,  h,  e,  b, −a, −d, −g, } {e,  g,  b, −c, −h, −d,  a,  f, } { g,  c, −d, −f,  a,  h,  b, −e, } { h,−a, −g,  b,  f, −c, −e,  d, } { f, −e, −a,  g, −d, −b,  h, −c, } { d,−h,  e, −a, −c,  g, −f,  b, } { b, −d,  f, −h,  g, −e,  c, −a, }where {a, b, c, d, e, f, g, h}={17, 32, 46, 60, 71, 78, 85, 86}16-point DST-7:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { c, f,  i,  l,  o,  o,  l,  i,  f,  c,  0, −c, −f, −i, −l, −o, } { e,  j, o,  m,  h,  c, −b, −g, −l, −p, −k, −f, −a,  d,  i,  n, } { g,  n,  l, e, −b, −i, −p, −j, −c,  d,  k,  o,  h,  a, −f, −m, } { i,  o,  f, −c,−l, −l, −c,  f,  o,  i,  0, −i, −o, −f,  c,  l, } { k,  k,  0, −k, −k, 0,  k,  k,  0, −k, −k,  0,  k,  k,  0, −k, } { m,  g, −f, −n, −a,  l, h, −e, −o, −b,  k,  i, −d, −p, −c,  j, } { o,  c, −l, −f,  i,  i, −f,−l,  c,  o,  0, −o, −c,  l,  f, −i, } { p, −a, −o,  b,  n, −c, −m,  d, l, −e, −k,  f,  j, −g, −i,  h, } { n, −e, −i,  j,  d, −o,  a,  m, −f,−h,  k,  c, −p,  b,  l, −g, } { l, −i, −c,  o, −f, −f,  o, −c, −i,  l, 0, −l,  i,  c, −o,  f, } { j, −m,  c,  g, −p,  f,  d, −n,  i,  a, −k, l, −b, −h,  o, −e, } { h, −p,  i, −a, −g,  o, −j,  b,  f, −n,  k, −c,−e,  m, −l,  d, } { f, −l,  o, −i,  c,  c, −i,  o, −l,  f,  0, −f,  l,−o,  i, −c, } { d, −h,  l, −p,  m, −i,  e, −a, −c,  g, −k,  o, −n,  j,−f,  b, } { b, −d,  f, −h,  j, −l,  n, −p,  o, −m,  k, −i,  g, −e,  c,−a, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={9, 17, 25, 33,41, 49, 56, 62, 66, 72, 77, 81, 83, 87, 89, 90}32-point DST-7:

 { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w,x, y, z, A, B, C, D, E, F, }  { c, f, i, l, o, r, u, x, A, D, F, C, z,w, t, q, n, k, h, e, b, −a, −d, −g, −j, −m, −p, −s, −v, −y, −B, −E, }  {e, j, o, t, y, D, D, y, t, o, j, e, 0, −e, −j, −o, −t, −y, −D, −D, − y,−t, −o, −j, −e, 0, e, j, o, t, y, D, }  { g, n, u, B, D, w, p, i, b, −e,−l, −s, −z, −F, −y, −r, −k, −d, c, j, q, x, E, A, t, m, f, −a, −h, −o,−v, −C, }  { i, r, A, C, t, k, b, −g, −p, −y, −E, −v, −m, −d, e, n, w,F, x, o, f, −c, −l, −u, −D, −z, −q, −h, a, j, s, B, }  { k, v, F, u, j,−a, −l, −w, −E, −t, −i, b, m, x, D, s, h, −c, −n, −y, − C, −r, −g, d, o,z, B, q, f, −e, −p, −A, }  { m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z,m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, }  { o,D, t, e, −j, −y, −y, −j, e, t, D, o, 0, −o, −D, −t, −e, i, y, y, j, −e,−t, −D, −o, 0, o, D, t, e, −j, −y, }  { q, E, n, −c, −t, −B, −k, f, w,y, h, −i, −z, −v, −e, l, C, s, b, −o, − F, −p, a, r, D, m, −d, −u, −A,−j, g, x, }  { s, A, h, −k, −D, −p, c, v, x, e, −n, −F, −m, f, y, u, b,−q, −C, −j, i, B, r, −a, −t, −z, −g, l, E, o, −d, −w, }  { u, w, b, −s,−y, −d, q, A, f, −o, −C, −h, m, E, j, −k, −F, −l, i, D, n, −g, −B, −p,e, z, r, −c, −x, −t, a, v, }  { w, s, −d, −A, −o, h, E, k, −l, −D, −g,p, z, c, −t, −v, a, x, r, −e, − B, −n, i, F, j, −m, −C, −f, q, y, b, −u,}  { y, o, −j, −D, −e, t, t, −e, −D, −j, o, y, 0, −y, −o, i, D, e, −t,−t, e, D, j, −o, −y, 0, y, o, −j, −D, −e, t, }  { A, k, −p, −v, e, F, f,−u, −q, j, B, a, −z, −l, o, w, −d, −E, −g, t, r, −i, −C, −b, y, m, −n,−x, c, D, h, −s, }  { C, g, −v, −n, o, u, −h, −B, a, D, f, −w, −m, p, t,−A, b, E, e, − x, −l, q, s, −j, −z, c, F, d, −y, −k, r, }  { E, c, −B,−f, y, i, −v, −l, s, o, −p, −r, m, u, g, A, −d, −D, a, F, b, −C, −e, z,h, −w, −k, t, n, −q, }  { F, −a, −E, b, D, −c, −C, d, B, −e, −A, f, z,−g, −y, h, x, −i, −w, j, v, −k, −u, l, t, −m, −s, n, r, −o, −q, p, }  {D, −e, −y, j, t, −o, −o, t, j, −y, −e, D, 0, −D, e, y, −j, −t, o, o, −t, −j, y, e, −D, 0, D, −e, −y, j, t, −o, }  { B, −i, −s, r, j, −A, −a,C, −h, −t, q, k, −z, −b, D, −g, −u, p, l, −y, − c, E, −f, −v, o, m, −x,−d, F, −e, −w, n, }  { z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m, −m, z,0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m, }  { x, −q,−g, E, −j, −n, A, −c, −u, t, d, −B, m, k, −D, f, r, −w, −a, y, − p, −h,F, −i, −o, z, −b, −v, s, e, −C, l, }  { v, −u, −a, w, −t, −b, x, −s, −c,y, −r, −d, z, −q, −e, A, −p, −f, B, −o, − g, C, −n, −h, D, −m, −i, E,−l, −j, F, −k, }  { t, −y, e, o, −D, j, j, −D, o, e, −y, t, 0, −t, y,−e, −o, D, −j, −j, D, −o, −e, y, −t, 0, t, −y, e, o, −D, j, }  { r, −C,k, g, −y, v, −d, −n, F, −o, −c, u, −z, h, j, −B, s, −a, −q, D, − l, −f,x, −w, e, m, −E, p, b, −t, A, −i, }  { p, −F, q, −a, −o, E, −r, b, n,−D, s, −c, −m, C, −t, d, l, −B, u, −e, − k, A, −v, f, j, −z, w, −g, −i,y, −x, h, }  { n, −B, w, −i, −e, s, −F, r, −d, −j, x, −A, in, a, −o, C,−v, h, f, −t, E, −q, c, k, −y, z, −l, −b, p, −D, u, −g, }  { l, −x, C,−q, e, g, −s, E, −v, j, b, −n, z, −A, o, −c, −i, u, −F, t, − h, −d, p,−B, y, −m, a, k, −w, D, −r, f, }  { j, −t, D, −y, o, −e, −e, o, −y, D,−t, i, 0, −i, t, −D, y, −o, e, e, − o, y, −D, t, −j, 0, j, −t, D, −y, o,−e, }  { h, −p, x, −F, y, −q, i, −a, −g, o, −w, E, −z, r, −j, b, f, −n,v, −D, A, −s, k, −c, −e, m, −u, C, −B, t, −l, d, }  { f, −l, r, −x, D,−C, w, −q, k, −e, −a, g, −m, s, −y, E, −B, v, −p, −j, − d, −b, h, −n, t,−z, F, −A, u, −o, i, −c, }  { d, −h, l, −p, t, −x, B, −F, C, −y, u, −q,m, −i, e, −a, −c, g, −k, o, − s, w, −A, E, −D, z, −v, r, −n, j, −f, b, } { b, −d, f, −h, j, −l, n, −p, r, −t, v, −x, z, −B, D, −F, E, −C, A, −y,w, −u, s, −q, o, −m, k, −i, g, −e, c, −a, }where {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p, q, r, s, t, u, v, w,x, y, z, A, B, C, D, E, F}={4, 9, 13, 17, 21, 26, 30, 34, 38, 42, 45,50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 88, 88,89, 90, 90}4-point DCT-8:

  { a, b, c, d, } { b, 0, −b, −b, } { c, −b, −d, a, } { d, −b, a, −c, }where {a, b, c, d}={84,74,55,29}8-point DCT-8:

  { a, b, c, d, e, f, g, h, } { b, e, h, −g, −d, −a, −c, −f, } { c, h,−e, −a, −f, g, b, d, } { d, −g, −a, −h, c, e, −f, −b, } { e, −d, −f, c,g, −b, −h, a, } { f, −a, g, e, −b, h, d, −c, } { g, −c, b, −f, −h, d,−a, e, } { h, −f, d, −b, a, −c, e, −g, }where {a, b, c, d, e, f, g, h}={86,85,78,71,60,46,32,17}16-point DCT-8:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { b, e,  h,  k,  n,  0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c,  h, m, −p, −k, −f, −a, −e, −j, −o,  n,  i,  d,  b,  g,  l, } { d,  k, −p,−i, −b, −f, −m,  n,  g,  a,  h,  o, −l, −e, −c, −j, } { e,  n, −k, −b,−h,  0,  h,  b,  k, −n, −e, −e, −n,  k,  b,  h, } { f,  0, −f, −f,  0, f,  f,  0, −f, −f,  0,  f,  f,  0, −f, −f, } { g, −n, −a, −m,  h,  f,−o, −b, −l,  i,  e, −p, −c, −k,  j,  d, } { h, −k, −e,  n,  b,  0, −b,−n,  e,  k, −h, −h,  k,  e, −n, −b, } { i, −h, −j,  g,  k, −f, −l,  e, m, −d, −n,  c,  o, −b, −p,  a, } { j, −e, −o,  a, −n, −f,  i,  k, −d,−p,  b, −m, −g,  h,  l, −c, } { k, −b,  n,  h, −e,  0,  e, −h, −n,  b,−k, −k,  b, −n, −h,  e, } { l, −b,  i,  o, −e,  f, −p, −h,  c, −m, −k, a, −j, −n,  d, −g, } { m, −e,  d, −l, −n,  f, −c,  k,  o, −g,  b, −j,−p,  h, −a,  i, } { n, −h,  b, −e,  k,  0, −k,  e, −b,  h, −n, −n,  h,−b,  e, −k, } { o, −k,  g, −c,  b, −f,  j, −n, −p,  l, −h,  d, −a,  e,−i,  m, } { p, −n,  l, −j,  h, −f,  d, −b,  a, −c,  e, −g,  i, −k,  m,−o, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o,p}={90,89,87,83,81,77,72,66,62,56,49,41,33,25,17, 9}32-point DCT-8:

 { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w,x, y, z, A, B, C, D, E, F, }  { b, e, h, k, n, q, t, w, z, C, F, −E, −B,−y, −v, −s, −p, −m, −j, −g, − d, −a, −c, −f, −i, −l, −o, −r, −u, −x, −A,−D, }  { c, h, m, r, w, B, 0, −B, −w, −r, −m, −h, −c, −c, −h, −m, −r,−w, −B, 0, B, w, r, m, h, c, c, h, m, r, w, B, }  { d, k, r, y, F, −A,−t, −m, −f, −b, −i, −p, −w, −D, C, v, o, h, a, g, n, u, B, −E, −x, −q,−j, −c, −e, −l, −s, −z, }  { e, n, w, F, −y, −p, −g, −c, −l, −u, −D, A,r, i, a, j, s, B, −C, −t, − k, −b, −h, −q, −z, E, v, m, d, f, o, x, }  {f, q, B, −A, −p, −e, −g, −r, −C, z, o, d, h, s, D, −y, −n, −c, −i, −t, −E, x, m, b, j, u, F, −w, −l, −a, −k, −v, }  { g, t, 0, −t, −g, −g, −t,0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0,t, g, g, t, }  { h, w, −B, −m, −c, −r, 0, r, c, m, B, −w, −h, −h, −w, B,m, c, r, 0, − r, −c, −m, −B, w, h, h, w, −B, −m, −c, −r, }  { i, z, −w,−f, −l, −C, t, c, o, F, −q, −a, −r, E, n, d, u, −B, −k, −g, − x, y, h,j, A, −v, −e, −m, −D, s, b, p, }  { j, C, −r, −b, −u, z, g, m, F, −o,−e, −x, w, d, p, −E, −l, −h, −A, t, a, s, −B, −i, −k, −D, q, c, v, −y,−f, −n, }  { k, F, −m, −i, −D, o, g, B, −q, −e, −z, s, c, x, −u, −a, −v,w, b, t, − y, −d, −r, A, f, p, −C, −h, −n, E, j, l, }  { l, −E, −h, −p,A, d, t, −w, −a, −x, s, e, B, −o, −i, −F, k, m, −D, −g, − q, z, c, u,−v, −b, −y, r, f, C, −n, −j, }  { m, −B, −c, −w, r, h, 0, −h, −r, w, c,B, −m, −m, B, c, e, −r, −h, 0, h, r, −w, −c, −B, m, m, −B, −c, −w, r, h,}  { n, −y, −c, −D, i, s, −t, −h, E, d, x, −o, −m, z, b, C, −j, −r, u,g, − F, −e, −w, p, l, −A, −a, −B, k, q, −v, −f, }  { o, −v, −h, C, a, D,−g, −w, n, p, −u, −i, B, b, E, −f, −x, m, q, −t, − j, A, c, F, −e, −y,l, r, −s, −k, z, d, }  { p, −s, −m, v, j, −y, −g, B, d, −E, −a, −F, c,C, −f, −z, i, w, −l, −t, o, q, −r, −n, u, k, −x, −h, A, e, D, −b, }  {q, −p, −r, o, s, −n, −t, m, u, −l, −v, k, w, −j, −x, i, y, −h, −z, g, A,−f, −B, e, C, −d, −D, c, E, −b, −F, a, }  { r, −m, −w, h, B, −c, 0, c,−B, −h, w, m, −r, −r, m, w, −h, −B, c, 0, − c, B, h, −w, −m, r, r, −m,−w, h, B, −c, }  { s, −j, −B, a, −C, −i, t, r, −k, −A, b, −D, −h, u, q,−l, −z, c, −E, −g, v, p, −m, −y, d, −F, −f, w, o, −n, −x, e, }  { t, −g,0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0,g, −t, −t, g, 0, −g, t, t, −g, }  { u, −d, B, n, −k, −E, g, −r, −x, a,−y, −q, h, −F, −j, o, A, −c, v, t, − e, C, m, −l, −D, f, −s, −w, b, −z,−p, i, }  { v, −a, w, u, −b, x, t, −c, y, s, −d, z, r, −e, A, q, −f, B,p, −g, C, o, −h, D, n, −i, E, m, −j, F, l, −k, }  { w, −c, r, B, −h, m,0, −m, h, −B, −r, c, −w, −w, c, −r, −B, h, −m, 0 m, −h, B, r, −c, w, w,−c, r, B, −h, m, }  { x, −f, m, −E, −q, b, −t, −B, j, −i, A, u, −c, p,F, −n, e, −w, −y, g, − l, D, r, −a, s, C, −k, h, −z, −v, d, −o, }  { y,−i, h, −x, −z, j, −g, w, A, −k, f, −v, −B, l, −e, u, C, −m, d, −t, − D,n, −c, s, E, −o, b, −r, −F, p, −a, q, }  { z, −l, c, −q, E, u, −g, h,−v, −D, p, −b, m, −A, −y, k, −d, r, −F, −t, f, −i, w, C, −o, a, −n, B,x, −j, e, −s, }  { A, −o, c, −j, v, F, −t, h, −e, q, −C, −y, m, −a, l,−x, −D, r, −f, g, − s, E, w, −k, b, −n, z, B, −p, d, −i, u, }  { B, −r,h, −c, m, −w, 0, w, −m, c, −h, r, −B, −B, r, −h, c, −m, w, 0, − w, m,−c, h, −r, B, B, −r, h, −c, m, −w, }  { C, −u, m, −e, d, −l, t, −B, −D,v, −n, f, −c, k, −s, A, E, −w, o, g, b, −j, r, −z, −F, x, −p, h, −a, i,−q, y, }  { D, −x, r, −l, f, −a, g, −m, s, −y, E, C, −w, q, −k, e, −b,h, −n, t, − z, F, B, −v, p, −j, d, −c, i, −o, u, −A, }  { E, −A, w, −s,o, −k, g, −c, b, −f, j, −n, r, −v, z, −D, −F, B, −x, t, − p, l, −h, d,−a, e, −i, m, −q, u, −y, C, }  { F, −D, B, −z, x, −v, t, −r, p, −n, l,−j, h, −f, d, −b, a, −c, e, −g, −k, m, −o, q, −s, u, −w, y, −A, C, −E, }where {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p, q, r, s, t, u, v, w,x, y, z, A, B, C, D, E,F}={90,90,89,88,88,86,85,84,82,80,78,77,74,72,68,66,63,60,56,53,50,45,42,38,34,30,26,21,17,13,9,4}

FIG. 2 is a simplified block diagram of a communication system (200)according to an embodiment. The communication system (200) may includeat least two terminals (210-220) interconnected via a network (250). Forunidirectional transmission of data, a first terminal (210) may codevideo data at a local location for transmission to the other terminal(220) via the network (250). The second terminal (220) may receive thecoded video data of the other terminal from the network (250), decodethe coded data and display the recovered video data. Unidirectional datatransmission may be common in media serving applications and the like.

FIG. 2 illustrates a second pair of terminals (230, 240) provided tosupport bidirectional transmission of coded video that may occur, forexample, during videoconferencing. For bidirectional transmission ofdata, each terminal (230, 240) may code video data captured at a locallocation for transmission to the other terminal via the network (250).Each terminal (230, 240) also may receive the coded video datatransmitted by the other terminal, may decode the coded data and maydisplay the recovered video data at a local display device.

In FIG. 2 , the terminals (210-240) may be illustrated as servers,personal computers and smart phones but the principles of embodimentsare not so limited. Embodiments find application with laptop computers,tablet computers, media players and/or dedicated video conferencingequipment. The network (250) represents any number of networks thatconvey coded video data among the terminals (210-240), including forexample wireline and/or wireless communication networks. Thecommunication network (250) may exchange data in circuit-switched and/orpacket-switched channels. Representative networks includetelecommunications networks, local area networks, wide area networksand/or the Internet. For the purposes of the present discussion, thearchitecture and topology of the network (250) may be immaterial to theoperation of embodiments unless explained herein below.

FIG. 3 is a diagram of a placement of a video encoder and a videodecoder in a streaming environment, according to an embodiment. Thedisclosed subject matter can be equally applicable to other videoenabled applications, including, for example, video conferencing,digital TV, storing of compressed video on digital media including CD,DVD, memory stick and the like, and so on.

A streaming system may include a capture subsystem (313) that caninclude a video source (301), for example a digital camera, creating,for example, an uncompressed video sample stream (302). That samplestream (302), depicted as a bold line to emphasize a high data volumewhen compared to encoded video bitstreams, can be processed by anencoder (303) coupled to the camera (301). The encoder (303) can includehardware, software, or a combination thereof to enable or implementaspects of the disclosed subject matter as described in more detailbelow. The encoded video bitstream (304), depicted as a thin line toemphasize the lower data volume when compared to the sample stream, canbe stored on a streaming server (305) for future use. One or morestreaming clients (306, 308) can access the streaming server (305) toretrieve copies (307, 309) of the encoded video bitstream (304). Aclient (306) can include a video decoder (310) which decodes theincoming copy of the encoded video bitstream (307) and creates anoutgoing video sample stream (311) that can be rendered on a display(312) or other rendering device (not depicted). In some streamingsystems, the video bitstreams (304, 307, 309) can be encoded accordingto certain video coding/compression standards. Examples of thosestandards include ITU-T Recommendation H.265. Under development is avideo coding standard informally known as VVC. The disclosed subjectmatter may be used in the context of VVC.

FIG. 4 is a functional block diagram of a video decoder (310) accordingto an embodiment.

A receiver (410) may receive one or more codec video sequences to bedecoded by the decoder (310); in the same or an embodiment, one codedvideo sequence at a time, where the decoding of each coded videosequence is independent from other coded video sequences. The codedvideo sequence may be received from a channel (412), which may be ahardware/software link to a storage device which stores the encodedvideo data. The receiver (410) may receive the encoded video data withother data, for example, coded audio data and/or ancillary data streams,that may be forwarded to their respective using entities (not depicted).The receiver (410) may separate the coded video sequence from the otherdata. To combat network jitter, a buffer memory (415) may be coupled inbetween receiver (410) and entropy decoder/parser (420) (“parser”henceforth). When receiver (410) is receiving data from a store/forwarddevice of sufficient bandwidth and controllability, or from anisosychronous network, the buffer (415) may not be needed, or can besmall. For use on best effort packet networks such as the Internet, thebuffer (415) may be required, can be comparatively large and canadvantageously of adaptive size.

The video decoder (310) may include a parser (420) to reconstructsymbols (421) from the entropy coded video sequence. Categories of thosesymbols include information used to manage operation of the decoder(310), and potentially information to control a rendering device such asa display (312) that is not an integral part of the decoder but can becoupled to it, as was shown in FIG. 4 . The control information for therendering device(s) may be in the form of Supplementary EnhancementInformation (SEI messages) or Video Usability Information (VUI)parameter set fragments (not depicted). The parser (420) mayparse/entropy-decode the coded video sequence received. The coding ofthe coded video sequence can be in accordance with a video codingtechnology or standard, and can follow principles well known to a personskilled in the art, including variable length coding, Huffman coding,arithmetic coding with or without context sensitivity, and so forth. Theparser (420) may extract from the coded video sequence, a set ofsubgroup parameters for at least one of the subgroups of pixels in thevideo decoder, based upon at least one parameter corresponding to thegroup. Subgroups can include Groups of Pictures (GOPs), pictures, tiles,slices, macroblocks, Coding Units (CUs), blocks, Transform Units (TUs),Prediction Units (PUs) and so forth. The entropy decoder/parser may alsoextract from the coded video sequence information such as transformcoefficients, quantizer parameter (QP) values, motion vectors, and soforth.

The parser (420) may perform entropy decoding/parsing operation on thevideo sequence received from the buffer (415), so to create symbols(421). The parser (420) may receive encoded data, and selectively decodeparticular symbols (421). Further, the parser (420) may determinewhether the particular symbols (421) are to be provided to a MotionCompensation Prediction unit (453), a scaler/inverse transform unit(451), an Intra Prediction unit (452), or a loop filter unit (454).

Reconstruction of the symbols (421) can involve multiple different unitsdepending on the type of the coded video picture or parts thereof (suchas: inter and intra picture, inter and intra block), and other factors.Which units are involved, and how, can be controlled by the subgroupcontrol information that was parsed from the coded video sequence by theparser (420). The flow of such subgroup control information between theparser (420) and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, decoder (310) can beconceptually subdivided into a number of functional units as describedbelow. In a practical implementation operating under commercialconstraints, many of these units interact closely with each other andcan, at least partly, be integrated into each other. However, for thepurpose of describing the disclosed subject matter, the conceptualsubdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit (451). Thescaler/inverse transform unit (451) receives quantized transformcoefficient as well as control information, including which transform touse, block size, quantization factor, quantization scaling matrices,etc. as symbol(s) (421) from the parser (420). It can output blockscomprising sample values that can be input into aggregator (455).

In some cases, the output samples of the scaler/inverse transform (451)can pertain to an intra coded block; that is: a block that is not usingpredictive information from previously reconstructed pictures, but canuse predictive information from previously reconstructed parts of thecurrent picture. Such predictive information can be provided by an intrapicture prediction unit (452). In some cases, the intra pictureprediction unit (452) generates a block of the same size and shape ofthe block under reconstruction, using surrounding already reconstructedinformation fetched from the current (partly reconstructed) picture(456). The aggregator (455), in some cases, adds, on a per sample basis,the prediction information the intra prediction unit (452) has generatedto the output sample information as provided by the scaler/inversetransform unit (451).

In other cases, the output samples of the scaler/inverse transform unit(451) can pertain to an inter coded, and potentially motion compensatedblock. In such a case, a Motion Compensation Prediction unit (453) canaccess reference picture memory (457) to fetch samples used forprediction. After motion compensating the fetched samples in accordancewith the symbols (421) pertaining to the block, these samples can beadded by the aggregator (455) to the output of the scaler/inversetransform unit (in this case called the residual samples or residualsignal) so to generate output sample information. The addresses withinthe reference picture memory form where the motion compensation unitfetches prediction samples can be controlled by motion vectors,available to the motion compensation unit in the form of symbols (421)that can have, for example X, Y, and reference picture components.Motion compensation also can include interpolation of sample values asfetched from the reference picture memory when sub-sample exact motionvectors are in use, motion vector prediction mechanisms, and so forth.

The output samples of the aggregator (455) can be subject to variousloop filtering techniques in the loop filter unit (454). Videocompression technologies can include in-loop filter technologies thatare controlled by parameters included in the coded video bitstream andmade available to the loop filter unit (454) as symbols (421) from theparser (420), but can also be responsive to meta-information obtainedduring the decoding of previous (in decoding order) parts of the codedpicture or coded video sequence, as well as responsive to previouslyreconstructed and loop-filtered sample values.

The output of the loop filter unit (454) can be a sample stream that canbe output to the render device (312) as well as stored in the referencepicture memory (456) for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used asreference pictures for future prediction. Once a coded picture is fullyreconstructed and the coded picture has been identified as a referencepicture (by, for example, parser (420)), the current reference picture(456) can become part of the reference picture buffer (457), and a freshcurrent picture memory can be reallocated before commencing thereconstruction of the following coded picture.

The video decoder (310) may perform decoding operations according to apredetermined video compression technology that may be documented in astandard, such as ITU-T Rec. H.265. The coded video sequence may conformto a syntax specified by the video compression technology or standardbeing used, in the sense that it adheres to the syntax of the videocompression technology or standard, as specified in the videocompression technology document or standard and specifically in theprofiles document therein. Also necessary for compliance can be that thecomplexity of the coded video sequence is within bounds as defined bythe level of the video compression technology or standard. In somecases, levels restrict the maximum picture size, maximum frame rate,maximum reconstruction sample rate (measured in, for example megasamplesper second), maximum reference picture size, and so on. Limits set bylevels can, in some cases, be further restricted through HypotheticalReference Decoder (HRD) specifications and metadata for HRD buffermanagement signaled in the coded video sequence.

In an embodiment, the receiver (410) may receive additional (redundant)data with the encoded video. The additional data may be included as partof the coded video sequence(s). The additional data may be used by thevideo decoder (310) to properly decode the data and/or to moreaccurately reconstruct the original video data. Additional data can bein the form of, for example, temporal, spatial, or signal-to-noise ratio(SNR) enhancement layers, redundant slices, redundant pictures, forwarderror correction codes, and so on.

FIG. 5 is a functional block diagram of a video encoder (303) accordingto an embodiment.

The encoder (303) may receive video samples from a video source (301)(that is not part of the encoder) that may capture video image(s) to becoded by the encoder (303).

The video source (301) may provide the source video sequence to be codedby the encoder (303) in the form of a digital video sample stream thatcan be of any suitable bit depth (for example: 8 bit, 10 bit, 12 bit, .. . ), any colorspace (for example, BT.601 Y CrCB, RGB, . . . ) and anysuitable sampling structure (for example Y CrCb 4:2:0, Y CrCb 4:4:4). Ina media serving system, the video source (301) may be a storage devicestoring previously prepared video. In a videoconferencing system, thevideo source (301) may be a camera that captures local image informationas a video sequence. Video data may be provided as a plurality ofindividual pictures that impart motion when viewed in sequence. Thepictures themselves may be organized as a spatial array of pixels,wherein each pixel can comprise one or more samples depending on thesampling structure, color space, etc. in use. A person skilled in theart can readily understand the relationship between pixels and samples.The description below focuses on samples.

According to an embodiment, the encoder (303) may code and compress thepictures of the source video sequence into a coded video sequence (543)in real time or under any other time constraints as required by theapplication. Enforcing appropriate coding speed is one function ofController (550). Controller controls other functional units asdescribed below and is functionally coupled to these units. The couplingis not depicted for clarity. Parameters set by controller can includerate control related parameters (picture skip, quantizer, lambda valueof rate-distortion optimization techniques, . . . ), picture size, groupof pictures (GOP) layout, maximum motion vector search range, and soforth. A person skilled in the art can readily identify other functionsof controller (550) as they may pertain to video encoder (303) optimizedfor a certain system design.

Some video encoders operate in what a person skilled in the art readilyrecognizes as a “coding loop.” As an oversimplified description, acoding loop can consist of the encoding part of an encoder (530)(“source coder” henceforth) (responsible for creating symbols based onan input picture to be coded, and a reference picture(s)), and a (local)decoder (533) embedded in the encoder (303) that reconstructs thesymbols to create the sample data that a (remote) decoder also wouldcreate (as any compression between symbols and coded video bitstream islossless in the video compression technologies considered in thedisclosed subject matter). That reconstructed sample stream is input tothe reference picture memory (534). As the decoding of a symbol streamleads to bit-exact results independent of decoder location (local orremote), the reference picture buffer content is also bit exact betweenlocal encoder and remote encoder. In other words, the prediction part ofan encoder “sees” as reference picture samples exactly the same samplevalues as a decoder would “see” when using prediction during decoding.This fundamental principle of reference picture synchronicity (andresulting drift, if synchronicity cannot be maintained, for examplebecause of channel errors) is well known to a person skilled in the art.

The operation of the “local” decoder (533) can be the same as of a“remote” decoder (310), which has already been described in detail abovein conjunction with FIG. 4 . Briefly referring also to FIG. 4 , however,as symbols are available and en/decoding of symbols to a coded videosequence by entropy coder (545) and parser (420) can be lossless, theentropy decoding parts of decoder (310), including channel (412),receiver (410), buffer (415), and parser (420) may not be fullyimplemented in local decoder (533).

An observation that can be made at this point is that any decodertechnology except the parsing/entropy decoding that is present in adecoder also necessarily needs to be present, in substantially identicalfunctional form, in a corresponding encoder. The description of encodertechnologies can be abbreviated as they are the inverse of thecomprehensively described decoder technologies. Only in certain areas amore detail description is required and provided below.

As part of its operation, the source coder (530) may perform motioncompensated predictive coding, which codes an input frame predictivelywith reference to one or more previously-coded frames from the videosequence that were designated as “reference frames.” In this manner, thecoding engine (532) codes differences between pixel blocks of an inputframe and pixel blocks of reference frame(s) that may be selected asprediction reference(s) to the input frame.

The local video decoder (533) may decode coded video data of frames thatmay be designated as reference frames, based on symbols created by thesource coder (530). Operations of the coding engine (532) mayadvantageously be lossy processes. When the coded video data may bedecoded at a video decoder (not shown in FIG. 4 ), the reconstructedvideo sequence typically may be a replica of the source video sequencewith some errors. The local video decoder (533) replicates decodingprocesses that may be performed by the video decoder on reference framesand may cause reconstructed reference frames to be stored in thereference picture cache (534). In this manner, the encoder (303) maystore copies of reconstructed reference frames locally that have commoncontent as the reconstructed reference frames that will be obtained by afar-end video decoder (absent transmission errors).

The predictor (535) may perform prediction searches for the codingengine (532). That is, for a new frame to be coded, the predictor (535)may search the reference picture memory (534) for sample data (ascandidate reference pixel blocks) or certain metadata such as referencepicture motion vectors, block shapes, and so on, that may serve as anappropriate prediction reference for the new pictures. The predictor(535) may operate on a sample block-by-pixel block basis to findappropriate prediction references. In some cases, as determined bysearch results obtained by the predictor (535), an input picture mayhave prediction references drawn from multiple reference pictures storedin the reference picture memory (534).

The controller (550) may manage coding operations of the video coder(530), including, for example, setting of parameters and subgroupparameters used for encoding the video data.

Output of all aforementioned functional units may be subjected toentropy coding in the entropy coder (545). The entropy coder translatesthe symbols as generated by the various functional units into a codedvideo sequence, by loss-less compressing the symbols according totechnologies known to a person skilled in the art as, for exampleHuffman coding, variable length coding, arithmetic coding, and so forth.

The transmitter (540) may buffer the coded video sequence(s) as createdby the entropy coder (545) to prepare it for transmission via acommunication channel (560), which may be a hardware/software link to astorage device that may store the encoded video data. The transmitter(540) may merge coded video data from the video coder (530) with otherdata to be transmitted, for example, coded audio data and/or ancillarydata streams (sources not shown).

The controller (550) may manage operation of the encoder (303). Duringcoding, the controller (550) may assign to each coded picture a certaincoded picture type, which may affect the coding techniques that may beapplied to the respective picture. For example, pictures often may beassigned as one of the following frame types:

An Intra Picture (I picture) may be one that may be coded and decodedwithout using any other frame in the sequence as a source of prediction.Some video codecs allow for different types of Intra pictures,including, for example Independent Decoder Refresh Pictures. A personskilled in the art is aware of those variants of I pictures and theirrespective applications and features.

A Predictive picture (P picture) may be one that may be coded anddecoded using intra prediction or inter prediction using at most onemotion vector and reference index to predict the sample values of eachblock.

A Bi-directionally Predictive Picture (B Picture) may be one that may becoded and decoded using intra prediction or inter prediction using atmost two motion vectors and reference indices to predict the samplevalues of each block. Similarly, multiple-predictive pictures can usemore than two reference pictures and associated metadata for thereconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality ofsample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 sampleseach) and coded on a block-by-block basis. Blocks may be codedpredictively with reference to other (already coded) blocks asdetermined by the coding assignment applied to the blocks' respectivepictures. For example, blocks of I pictures may be codednon-predictively or they may be coded predictively with reference toalready coded blocks of the same picture (spatial prediction or intraprediction). Pixel blocks of P pictures may be coded non-predictively,via spatial prediction or via temporal prediction with reference to onepreviously coded reference pictures. Blocks of B pictures may be codednon-predictively, via spatial prediction or via temporal prediction withreference to one or two previously coded reference pictures.

The video coder (303) may perform coding operations according to apredetermined video coding technology or standard, such as ITU-T Rec.H.265. In its operation, the video coder (303) may perform variouscompression operations, including predictive coding operations thatexploit temporal and spatial redundancies in the input video sequence.The coded video data, therefore, may conform to a syntax specified bythe video coding technology or standard being used.

In an embodiment, the transmitter (540) may transmit additional datawith the encoded video. The video coder (530) may include such data aspart of the coded video sequence. Additional data may comprisetemporal/spatial/SNR enhancement layers, other forms of redundant datasuch as redundant pictures and slices, Supplementary EnhancementInformation (SEI) messages, Visual Usability Information (VUI) parameterset fragments, and so on.

The 8-bit primary transform cores of DST-7 and DCT-8 in VVC may befurther tuned for better coding efficiency or accuracy.

For example, accordint to an embodiment, a set of 8-bit DST-7 and DCT-8transform cores are proposed. The following proposed methods may be usedseparately or combined in any order.

According to an embodiment, the transform core matrices may be:

32-point DST-7:

 {  a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p,  q, r,  s,  t,  u,  v,  w,  x,  y,  z,  A,  B,  C,  D,  E,  F,  }  {  c, f,  i,  l,  o,  r,  u,  x,  A,  D,  F,  C,  z,  w,  t,  q,  n,  k,  h, e,  b, −a, −d, −g, −j, −m, −p, −s, −v, −y, −B, −E,  }  {  e,  j,  o, t,  y,  D,  D,  y,  t,  o,  j,  e,  0, −e, −j, −o, −t, −y, −D, −D, −y,−t, −o, −j, −e,  0,  e,  j,  o,  t,  y,  D,  }  {  g,  n,  u,  B,  D, w,  p,  i,  b, −e, −l, −s, −z, −F, −y, −r, −k, −d,  c,  j,  q,  x,  E, A,  t,  m,  f, −a, −h, −o, −v, −C,  }  {  i,  r,  A,  C,  t,  k,  b,−g, −p, −y, −E, −v, −m, −d,  e,  n,  w,  F,  x,  o,  f, −c, −l, −u, −D,−z, −q, −h,  a,  j,  s,  B,  }  {  k,  v,  F,  u,  j, −a, −l, −w, −E,−t, −i,  b,  m,  x,  D,  s,  h, −c, −n, −y, −C, −r, −g,  d,  o,  z,  B, q,  f, −e, −p, −A,  }  {  m,  z,  z,  m,  0, −m, −z, −z, −m,  0,  m, z,  z,  m,  0, −m, −z, −z, −m,  0,  m,  z,  z,  m,  0, −m, −z, −z, −m, 0,  m,  z,  }  {  o,  D,  t,  e, −j, −y, −y, −j,  e,  t,  D,  o,  0,−o, −D, −t, −e,  j,  y,  y,  j, −e, −t, −D, −o,  0,  o,  D,  t,  e, −j,−y,  }  {  q,  E,  n, −c, −t, −B, −k,  f,  w,  y,  h, −i, −z, −v, −e, l,  C,  s,  b, −o, −F, −p,  a,  r,  D,  m, −d, −u, −A, −j,  g,  x,  } {  s,  A,  h, −k, −D, −p,  c,  v,  x,  e, −n, −F, −m,  f,  y,  u,  b,−q, −C, −j,  i,  B,  r, −a, −t, −z, −g,  l,  E,  o, −d, −w,  }  {  u, w,  b, −s, −y, −d,  q,  A,  f, −o, −C, −h,  m,  E,  j, −k, −F, −l,  i, D,  n, −g, −B, −p,  e,  z,  r, −c, −x, −t,  a,  v,  }  {  w,  s, −d,−A, −o,  h,  E,  k, −l, −D, −g,  p,  z,  c, −t, −v,  a,  x,  r, −e, −B,−n,  i,  F,  j, −m, −C, −f,  q,  y,  b, −u,  }  {  y,  o, −j, −D, −e, t,  t, −e, −D, −j,  o,  y,  0, −y, −o,  j,  D,  e, −t, −t,  e,  D,  j,−o, −y,  0,  y,  o, −j, −D, −e,  t,  }  {  A,  k, −p, −v,  e,  F,  f,−u, −q,  j,  B,  a, −z, −l,  o,  w, −d, −E, −g,  t,  r, −i, −C, −b,  y, m, −n, −x,  c,  D,  h, −s,  }  {  C,  g, −v, −n,  o,  u, −h, −B,  a, D,  f, −w, −m,  p,  t, −i, −A,  b,  E,  e, −x, −l,  q,  s, −j, −z,  c, F,  d, −y, −k,  r,  }  {  E,  c, −B, −f,  y,  i, −v, −l,  s,  o, −p,−r,  m,  u, −j, −x,  g,  A, −d, −D,  a,  F,  b, −C, −e,  z,  h, −w, −k, t,  n, −q,  }  {  F, −a, −E,  b,  D, −c, −C,  d,  B, −e, −A,  f,  z,−g, −y,  h,  x, −i, −w,  j,  v, −k, −u,  l,  t, −m, −s,  n,  r, −o, −q, p,  }  {  D, −e, −y,  j,  t, −o, −o,  t,  j, −y, −e,  D,  0, −D,  e, y, −j, −t,  o,  o, −t, −j,  y,  e, −D,  0,  D, −e, −y,  j,  t, −o,  } {  B, −i, −s,  r,  j, −A, −a,  C, −h, −t,  q,  k, −z, −b,  D, −g, −u, p,  l, −y, −c,  E, −f, −v,  o,  m, −x, −d,  F, −e, −w,  n,  }  {  z,−m, −m,  z,  0, −z,  m,  m, −z,  0,  z, −m, −m,  z,  0, −z,  m,  m, −z, 0,  z, −m, −m,  z,  0, −z,  m,  m, −z,  0,  z, −m,  }  {  x, −q, −g, E, −j, −n,  A, −c, −u,  t,  d, −B,  m,  k, −D,  f,  r, −w, −a,  y, −p,−h,  F, −i, −o,  z, −b, −v,  s,  e, −C,  l,  }  {  v, −u, −a,  w, −t,−b,  x, −s, −c,  y, −r, −d,  z, −q, −e,  A, −p, −f,  B, −o, −g,  C, −n,−h,  D, −m, −i,  E, −l, −j,  F, −k,  }  {  t, −y,  e,  o, −D,  j,  j,−D,  o,  e, −y,  t,  0, −t,  y, −e, −o,  D, −j, −j,  D, −o, −e,  y, −t, 0,  t, −y,  e,  o, −D,  j,  }  {  r, −C,  k,  g, −y,  v, −d, −n,  F,−o, −c,  u, −z,  h,  j, −B,  s, −a, −q,  D, −l, −f,  x, −w,  e,  m, −E, p,  b, −t,  A, −i,  }  {  p, −F,  q, −a, −o,  E, −r,  b,  n, −D,  s,−c, −m,  C, −t,  d,  l, −B,  u, −e, −k,  A, −v,  f,  j, −z,  w, −g, −i, y, −x,  h,  }  {  n, −B,  w, −i, −e,  s, −F,  r, −d, −j,  x, −A,  m, a, −o,  C, −v,  h,  f, −t  E, −q,  c,  k, −y,  z, −l, −b,  p, −D,  u,−g,  }  {  l, −x,  C, −q,  e,  g, −s,  E, −v,  j,  b, −n,  z, −A,  o,−c, −i,  u, −F,  t, −h, −d,  p, −B,  y, −m,  a,  k, −w,  D, −r,  f,  } {  j, −t,  D, −y,  o, −e, −e,  o, −y,  D, −t,  j,  0, −j,  t, −D,  y,−o,  e,  e, −o,  y, −D,  t, −j,  0,  j, −t,  D, −y,  o, −e,  }  {  h,−p,  x, −F,  y, −q,  i, −a, −g,  o, −w,  E, −z,  r, −j,  b,  f, −n,  v,−D,  A, −s,  k, −c, −e,  m, −u,  C, −B,  t, −l,  d,  }  {  f, −l,  r,−x,  D, −C,  w, −q,  k, −e, −a,  g, −m,  s, −y,  E, −B,  v, −p,  j, −d,−b,  h, −n,  t, −z,  F −A,  u, −o,  i, −c,  }  {  d, −h,  l, −p,  t, −x, B, −F,  C, −y,  u, −q,  m, −i,  e, −a, −c,  g, −k,  o, −s,  w, −A,  E,−D,  z, −v,  r, −n,  j, −f,  b,  }  {  b, −d,  f, −h,  j, −l,  n, −p, r, −t,  v, −x,  z, −B,  D, −F,  E, −C,  A, −y,  w, −u,  s, −q,  o, −m, k, −i,  g, −e,  c, −a,  }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v,w, x, y, z, A, B, C, D, E, F}={4, 9, 13, 17, 21, 26, 30, 34, 38, 42, 46,50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 87, 88,89, 90, 90}32-point DCT-8:

 {  a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p,  q, r,  s,  t,  u,  v,  w,  x,  y,  z,  A,  B,  C,  D,  E,  F,  }  {  b, e,  h,  k,  n,  q,  t,  w,  z,  C,  F, −E, −B, −y, −v, −s, −p, −m, −j,−g, −d, −a, −c, −f, −i, −l, −o, −r, −u, −x, −A, −D,  }  {  c,  h,  m, r,  w,  B,  0, −B, −w, −r, −m, −h, −c, −c, −h, −m, −r, −w, −B,  0,  B, w,  r,  m,  h,  c,  c,  h,  m,  r,  w,  B,  }  {  d,  k,  r,  y,  F,−A, −t, −m, −f, −b, −i, −p, −w, −D,  C,  v,  o,  h,  a,  g,  n,  u,  B,−E, −x, −q, −j, −c, −e, −l, −s, −z,  }  {  e,  n,  w,  F, −y, −p, −g,−c, −l, −u, −D,  A,  r,  i,  a,  j,  s,  B, −C, −t, −k, −b, −h, −q, −z, E,  v,  m,  d,  f,  o,  x,  }  {  f,  q,  B, −A, −p, −e, −g, −r, −C, z,  o,  d,  h,  s,  D, −y, −n, −c, −i, −t, −E,  x,  m,  b,  j,  u,  F,−w, −l, −a, −k, −v,  }  {  g,  t,  0, −t, −g, −g, −t,  0,  t,  g,  g, t,  0, −t, −g, −g, −t,  0,  t,  g,  g,  t,  0, −t, −g, −g, −t,  0,  t, g,  g,  t,  }  {  h,  w, −B, −m, −c, −r,  0,  r,  c,  m,  B, −w, −h,−h, −w,  B,  m,  c,  r,  0, −r, −c, −m, −B,  w,  h,  h,  w, −B, −m, −c,−r,  }  {  i,  z, −w, −f, −l, −C,  t,  c,  o,  F, −q, −a, −r,  E,  n, d,  u, −B, −k, −g, −x,  y,  h,  j,  A, −v, −e, −m, −D,  s,  b,  p,  } {  j,  C, −r, −b, −u,  z,  g,  m,  F, −o, −e, −x,  w,  d,  p, −E, −l,−h, −A,  t,  a,  s, −B, −i, −k, −D,  q,  c,  v, −y, −f, −n,  }  {  k, F, −m, −i, −D,  o,  g,  B, −q, −e, −z,  s,  c,  x, −u, −a, −v,  w,  b, t, −y, −d, −r,  A,  f,  p, −C, −h, −n,  E,  j,  l,  }  {  l, −E, −h,−p,  A,  d,  t, −w, −a, −x,  s,  e,  B, −o, −i, −F,  k,  m, −D, −g, −q, z,  c,  u, −v, −b, −y,  r,  f,  C, −n, −j,  }  {  m, −B, −c, −w,  r, h,  0, −h, −r,  w,  c,  B, −m, −m,  B,  c,  w, −r, −h,  0,  h,  r, −w,−c, −B,  m,  m, −B, −c, −w,  r,  h,  }  {  n, −y, −c, −D,  i,  s, −t,−h,  E,  d,  x, −o,  −m,  z,  b,  C, −j, −r,  u,  g, −F, −e, −w,  p,  l,−A, −a, −B,  k,  q, −v, −f,  }  {  o, −v, −h,  C,  a,  D, −g, −w,  n, p, −u, −i,  B,  b,  E, −f, −x,  m,  q, −t, −j,  A,  c,  F, −e, −y,  l, r, −s, −k,  z,  d,  }  {  p, −s, −m,  v,  j, −y, −g,  B,  d, −E, −a,−F,  c,  C, −f, −z,  i,  w, −l, −t,  o,  q, −r, −n,  u,  k, −x, −h,  A, e, −D, −b,  }  {  q, −p, −r,  o,  s, −n, −t,  m,  u, −l, −v,  k,  w,−j, −x,  i,  y, −h, −z,  g,  A, −f, −B,  e,  C, −d, −D,  c,  E, −b, −F, a,  }  {  r, −m, −w,  h,  B, −c,  0,  c, −B, −h,  w,  m, −r, −r,  m, w, −h, −B,  c,  0, −c,  B,  h, −w, −m,  r,  r, −m, −w,  h,  B, −c,  } {  s, −j, −B,  a, −C, −i,  t,  r, −k, −A,  b, −D, −h,  u,  q, −l, −z, c, −E, −g,  v,  p, −m, −y,  d, −F, −f,  w,  o, −n, −x,  e,  }  {  t,−g,  0,  g, −t, −t,  g,  0, −g,  t,  t, −g,  0,  g, −t, −t,  g,  0, −g, t,  t, −g,  0,  g, −t, −t,  g,  0, −g,  t,  t, −g,  }  {  u, −d,  B, n, −k, −E,  g, −r, −x,  a, −y, −q,  h, −F, −j,  o,  A, −c,  v,  t, −e, C,  m, −l, −D,  f, −s, −w,  b, −z, −p,  i,  }  {  v, −a,  w,  u, −b, x,  t, −c,  y,  s, −d,  z,  r, −e,  A,  q, −f,  B,  p, −g,  C,  o, −h, D,  n, −i,  E,  m, −j,  F,  l, −k,  }  {  w, −c,  r,  B, −h,  m,  0,−m,  h, −B, −r,  c, −w, −w,  c, −r, −B,  h, −m,  0,  m, −h,  B,  r, −c, w,  w, −c,  r,  B, −h,  m,  }  {  x, −f,  m, −E, −q,  b, −t, −B,  j,−i,  A,  u, −c,  p,  F, −n,  e, −w, −y,  g, −1,  D,  r, −a,  s,  C, −k, h, −z, −v,  d, −o,  }  {  y, −i,  h, −x, −z,  j, −g,  w,  A, −k,  f,−v, −B,  l, −e,  u,  C, −m,  d, −t, −D,  n, −c,  s,  E, −o,  b, −r, −F, p, −a,  q,  }  {  z, −l,  c, −q,  E,  u, −g,  h, −v, −D,  p, −b,  m,−A, −y,  k, −d,  r, −F, −t,  f, −i,  w,  C, −o,  a, −n,  B,  x, −j,  e,−s,  }  {  A, −o,  c, −j,  v,  F, −t,  h, −e,  q, −C, −y,  m, −a,  l,−x, −D,  r, −f,  g, −s,  E,  w, −k,  b, −n,  z,  B, −p,  d, −i,  u,  } {  B, −r,  h, −c,  m, −w,  0,  w, −m,  c, −h,  r, −B, −B,  r, −h,  c,−m,  w,  0, −w,  m, −c,  h, −r,  B,  B, −r,  h, −c,  m, −w,  }  {  C,−u,  m, −e,  d, −l,  t, −B, −D,  v, −n,  f, −c,  k, −s,  A,  E, −w,  o,−g,  b, −j,  r, −z, −F,  x, −p,  h, −a,  i, −q,  y,  }  {  D, −x,  r,−l,  f, −a,  g, −m,  s, −y,  E,  C, −w,  q, −k,  e, −b,  h, −n,  t, −z, F,  B, −v,  p, −j,  d, −c,  i, −o,  u, −A,  }  {  E, −A,  w, −s,  o,−k,  g, −c,  b, −f,  j, −n,  r, −v,  z, −D, −F,  B, −x,  t, −p,  l, −h, d, −a,  e, −i,  m, −q,  u, −y,  C,  }  {  F, −D,  B, −z,  x, −v,  t,−r,  p, −n,  l, −j,  h, −f,  d, −b,  a, −c,  e, −g,  i, −k,  m, −o,  q,−s,  u, −w,  y, −A,  C, −E,  }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v,w, x, y, z, A, B, C, D, E, F}={90, 90, 89, 88, 87, 86, 85, 84, 82, 80,78, 77, 74, 72, 68, 66, 63, 60, 56, 53, 50, 46, 42, 38, 34, 30, 26, 21,17, 13, 9, 4}

According to another embodiment, the transform core matrices may be:

16-point DST-7:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { c, f,  i,  l,  o,  o,  l,  i,  f,  c,  0, −c, −f, −i, −l, −o, } { e,  j, o,  m,  h,  c, −b, −g, −l, −p, −k, −f, −a,  d,  i,  n, } { g,  n,  l, e, −b, −i, −p, −j, −c,  d,  k,  o,  h,  a, −f, −m, } { i,  o,  f, −c,−l, −l, −c,  f,  o,  i,  0, −i, −o, −f,  c,  l, } { k,  k,  0, −k, −k, 0,  k,  k,  0, −k, −k,  0,  k,  k,  0, −k, } { m,  g, −f, −n, −a,  l, h, −e, −o, −b,  k,  i, −d, −p, −c,  j, } { o,  c, −l, −f,  i,  i, −f,−l,  c,  o,  0, −o, −c,  l,  f, −i, } { p, −a, −o,  b,  n, −c, −m,  d, l, −e, −k,  f,  j, −g, −i,  h, } { n, −e, −i,  j,  d, −o,  a,  m, −f,−h,  k,  c, −p,  b,  l, −g, } { l, −i, −c,  o, −f, −f,  o, −c, −i,  l, 0, −l,  i,  c, −o,  f, } { j, −m,  c,  g, −p,  f,  d, −n,  i,  a, −k, l, −b, −h,  o, −e, } { h, −p,  i, −a, −g,  o, −j,  b,  f, −n,  k, −c,−e,  m, −l,  d, } { f, −l,  o, −i,  c,  c, −i,  o, −l,  f,  0, −f,  l,−o,  i, −c, } { d, −h,  l, −p,  m, −i,  e, −a, −c,  g, −k,  o, −n,  j,−f,  b, } { b, −d,  f, −h,  j, −l,  n, −p,  o, −m,  k, −i,  g, −e,  c,−a, }where {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p}={9, 17, 25, 33, 41,48, 55, 61, 68, 72, 77, 81, 85, 86, 88, 89}16-point DCT-8:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { b, e,  h,  k,  n,  0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c,  h, m, −p, −k, −f, −a, −e, −j, −o,  n,  i,  d,  b,  g,  l, } { d,  k, −p,−i, −b, −f, −m,  n,  g,  a,  h,  o, −l, −e, −c, −j, } { e,  n, −k, −b,−h,  0,  h,  b,  k, −n, −e, −e, −n,  k,  b,  h, } { f,  0, −f, −f,  0, f,  f,  0, −f, −f,  0,  f,  f,  0, −f, −f, } { g, −n, −a, −m,  h,  f,−o, −b, −l,  i,  e, −p, −c, −k,  j,  d, } { h, −k, −e,  n,  b,  0, −b,−n,  e,  k, −h, −h,  k,  e, −n, −b, } { i, −h, −j,  g,  k, −f, −l,  e, m, −d, −n,  c,  o, −b, −p,  a, } { j, −e, −o,  a, −n, −f,  i,  k, −d,−p,  b, −m, −g,  h,  l, −c, } { k, −b,  n,  h, −e,  0,  e, −h, −n,  b,−k, −k,  b, −n, −h,  e, } { l, −b,  i,  o, −e,  f, −p, −h,  c, −m, −k, a, −j, −n,  d, −g, } { m, −e,  d, −l, −n,  f, −c,  k,  o, −g,  b, −j,−p,  h, −a,  i, } { n, −h,  b, −e,  k,  0, −k,  e, −b,  h, −n, −n,  h,−b,  e, −k, } { o, −k,  g, −c,  b, −f,  j, −n, −p,  l, −h,  d, −a,  e,−i,  m, } { p, −n,  l, −j,  h, −f,  d, −b,  a, −c,  e, −g,  i, −k,  m,−o, }where {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p}={89, 88, 86, 85, 81,77, 72, 68, 61, 55, 48, 41, 33, 25, 17, 9}

According to another embodiment, the transform core matrices may be:

16-point DST-7:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { c, f,  i,  l,  o,  o,  l,  i,  f,  c,  0, −c, −f, −i, −l, −o, } { e,  j, o,  m,  h,  c, −b, −g, −l, −p, −k, −f, −a,  d,  i,  n, } { g,  n,  l, e, −b, −i, −p, −j, −c,  d,  k,  o,  h,  a, −f, −m, } { i,  o,  f, −c,−l, −l, −c,  f,  o,  i,  0, −i, −o, −f,  c,  l, } { k,  k,  0, −k, −k, 0,  k,  k,  0, −k, −k,  0,  k,  k,  0, −k, } { m,  g, −f, −n, −a,  l, h, −e, −o, −b,  k,  i, −d, −p, −c,  j, } { o,  c, −l, −f,  i,  i, −f,−l,  c,  o,  0, −o, −c,  l,  f, −i, } { p, −a, −o,  b,  n, −c, −m,  d, l, −e, −k,  f,  j, −g, −i,  h, } { n, −e, −i,  j,  d, −o,  a,  m, −f,−h,  k,  c, −p,  b,  l, −g, } { l, −i, −c,  o, −f, −f,  o, −c, −i,  l, 0, −l,  i,  c, −o,  f, } { j, −m,  c,  g, −p,  f,  d, −n,  i,  a, −k, l, −b, −h,  o, −e, } { h, −p,  i, −a, −g,  o, −j,  b,  f, −n,  k, −c,−e,  m, −l,  d, } { f, −l,  o, −i,  c,  c, −i,  o, −l,  f,  0, −f,  l,−o,  i, −c, } { d, −h,  l, −p,  m, −i,  e, −a, −c,  g, −k,  o, −n,  j,−f,  b, } { b, −d,  f, −h,  j, −l,  n, −p,  o, −m,  k, −i,  g, −e,  c,−a, }where {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p}={8, 17, 25, 33, 40,48, 55, 62, 68, 73, 77, 81, 85, 87, 88, 88}16-point DCT-8:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { b, e,  h,  k,  n,  0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c,  h, m, −p, −k, −f, −a, −e, −j, −o,  n,  i,  d,  b,  g,  l, } { d,  k, −p,−i, −b, −f, −m,  n,  g,  a,  h,  o, −l, −e, −c, −j, } { e,  n, −k, −b,−h,  0,  h,  b,  k, −n, −e, −e, −n,  k,  b,  h, } { f,  0, −f, −f,  0, f,  f,  0, −f, −f,  0,  f,  f,  0, −f, −f, } { g, −n, −a, −m,  h,  f,−o, −b, −l,  i,  e, −p, −c, −k,  j,  d, } { h, −k, −e,  n,  b,  0, −b,−n,  e,  k, −h, −h,  k,  e, −n, −b, } { i, −h, −j,  g,  k, −f, −l,  e, m, −d, −n,  c,  o, −b, −p,  a, } { j, −e, −o,  a, −n, −f,  i,  k, −d,−p,  b, −m, −g,  h,  l, −c, } { k, −b,  n,  h, −e,  0,  e, −h, −n,  b,−k, −k,  b, −n, −h,  e, } { l, −b,  i,  o, −e,  f, −p, −h,  c, −m, −k, a, −j, −n,  d, −g, } { m, −e,  d, −l, −n,  f, −c,  k,  o, −g,  b, −j,−p,  h, −a,  i, } { n, −h,  b, −e,  k,  0, −k,  e, −b,  h, −n, −n,  h,−b,  e, −k, } { o, −k,  g, −c,  b, −f,  j, −n, −p,  l, −h,  d, −a,  e,−i,  m, } { p, −n,  l, −j,  h, −f,  d, −b,  a, −c,  e, −g,  i, −k,  m,−o, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 87, 85,81, 77, 73, 68, 62, 55, 48, 40, 33, 25, 17, 8}

According to another embodiment, the transform core matrices may be:

16-point DST-7:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { c, f,  i,  l,  o,  o,  l,  i,  f,  c,  0, −c, −f, −i, −l, −o, } { e,  j, o,  m,  h,  c, −b, −g, −l, −p, −k, −f, −a,  d,  i,  n, } { g,  n,  l, e, −b, −i, −p, −j, −c,  d,  k,  o,  h,  a, −f, −m, } { i,  o,  f, −c,−l, −l, −c,  f,  o,  i,  0, −i, −o, −f,  c,  l, } { k,  k,  0, −k, −k, 0,  k,  k,  0, −k, −k,  0,  k,  k,  0, −k, } { m,  g, −f, −n, −a,  l, h, −e, −o, −b,  k,  i, −d, −p, −c,  j, } { o,  c, −l, −f,  i,  i, −f,−l,  c,  o,  0, −o, −c,  l,  f, −i, } { p, −a, −o,  b,  n, −c, −m,  d, l, −e, −k,  f,  j, −g, −i,  h, } { n, −e, −i,  j,  d, −o,  a,  m, −f,−h,  k,  c, −p,  b,  l, −g, } { l, −i, −c,  o, −f, −f,  o, −c, −i,  l, 0, −l,  i,  c, −o,  f, } { j, −m,  c,  g, −p,  f,  d, −n,  i,  a, −k, l, −b, −h,  o, −e, } { h, −p,  i, −a, −g,  o, −j,  b,  f, −n,  k, −c,−e,  m, −l,  d, } { f, −l,  o, −i,  c,  c, −i,  o, −l,  f,  0, −f,  l,−o,  i, −c, } { d, −h,  l, −p,  m, −i,  e, −a, −c,  g, −k,  o, −n,  j,−f,  b, } { b, −d,  f, −h,  j, −l,  n, −p,  o, −m,  k, −i,  g, −e,  c,−a, }

where {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p}={8, 16, 25, 33, 41,48, 55, 62, 68, 73, 77, 81, 84, 87, 88, 89}

16-point DCT-8:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { b, e,  h,  k,  n,  0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c,  h, m, −p, −k, −f, −a, −e, −j, −o,  n,  i,  d,  b,  g,  l, } { d,  k, −p,−i, −b, −f, −m,  n,  g,  a,  h,  o, −l, −e, −c, −j, } { e,  n, −k, −b,−h,  0,  h,  b,  k, −n, −e, −e, −n,  k,  b,  h, } { f,  0, −f, −f,  0, f,  f,  0, −f, −f,  0,  f,  f,  0, −f, −f, } { g, −n, −a, −m,  h,  f,−o, −b, −l,  i,  e, −p, −c, −k,  j,  d, } { h, −k, −e,  n,  b,  0, −b,−n,  e,  k, −h, −h,  k,  e, −n, −b, } { i, −h, −j,  g,  k, −f, −l,  e, m, −d, −n,  c,  o, −b, −p,  a, } { j, −e, −o,  a, −n, −f,  i,  k, −d,−p,  b, −m, −g,  h,  l, −c, } { k, −b,  n,  h, −e,  0,  e, −h, −n,  b,−k, −k,  b, −n, −h,  e, } { l, −b,  i,  o, −e,  f, −p, −h,  c, −m, −k, a, −j, −n,  d, −g, } { m, −e,  d, −l, −n,  f, −c,  k,  o, −g,  b, −j,−p,  h, −a,  i, } { n, −h,  b, −e,  k,  0, −k,  e, −b,  h, −n, −n,  h,−b,  e, −k, } { o, −k,  g, −c,  b, −f,  j, −n, −p,  l, −h,  d, −a,  e,−i,  m, } { p, −n,  l, −j,  h, −f,  d, −b,  a, −c,  e, −g,  i, −k,  m,−o, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={89, 88, 87, 84,81, 77, 73, 68, 62, 55, 48, 41, 33, 25, 16, 8}

According to another embodiment, the transform core matrices may be:

16-point DST-7:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { c, f,  i,  l,  o,  o,  l,  i,  f,  c,  0, −c, −f, −i, −l, −o, } { e,  j, o,  m,  h,  c, −b, −g, −l, −p, −k, −f, −a,  d,  i,  n, } { g,  n,  l, e, −b, −i, −p, −j, −c,  d,  k,  o,  h,  a, −f, −m, } { i,  o,  f, −c,−l, −l, −c,  f,  o,  i,  0, −i, −o, −f,  c,  l, } { k,  k,  0, −k, −k, 0,  k,  k,  0, −k, −k,  0,  k,  k,  0, −k, } { m,  g, −f, −n, −a,  l, h, −e, −o, −b,  k,  i, −d, −p, −c,  j, } { o,  c, −l, −f,  i,  i, −f,−l,  c,  o,  0, −o, −c,  l,  f, −i, } { p, −a, −o,  b,  n, −c, −m,  d, l, −e, −k,  f,  j, −g, −i,  h, } { n, −e, −i,  j,  d, −o,  a,  m, −f,−h,  k,  c, −p,  b,  l, −g, } { l, −i, −c,  o, −f, −f,  o, −c, −i,  l, 0, −l,  i,  c, −o,  f, } { j, −m,  c,  g, −p,  f,  d, −n,  i,  a, −k, l, −b, −h,  o, −e, } { h, −p,  i, −a, −g,  o, −j,  b,  f, −n,  k, −c,−e,  m, −l,  d, } { f, −l,  o, −i,  c,  c, −i,  o, −l,  f,  0, −f,  l,−o,  i, −c, } { d, −h,  l, −p,  m, −i,  e, −a, −c,  g, −k,  o, −n,  j,−f,  b, } { b, −d,  f, −h,  j, −l,  n, −p,  o, −m,  k, −i,  g, −e,  c,−a, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p 8, 16, 25, 33, 40,48, 55, 62, 68, 73, 77, 81, 84, 87, 88, 88}16-point DCT-8:

  { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, } { b, e, h, k, n,0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c, h, m, −p, −k, −f, −a,−e, −j, −o, n, i, d, b, g, l, } { d, k, −p, −i, −b, −f, −m, n, g, a, h,o, −l, −e, −c, −j, } { e, n, −k, −b, −h, 0, h, b, k, −n, −e, −e, −n, k,b, h, } { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0, −f, −f, } { g,−n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d, } { h, −k, −e, n,b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b, } { i, −h, −j, g, k, −f, −l,e, m, −d, −n, c, o, −b, −p, a, } { j, −e, −o, a, −n, −f, i, k, −d, −p,b, −m, −g, h, l, −c, } { k, −b, n, h, −e, 0, e, −h, −n, b, −k, −k, b,−n, −h, e, } { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n, d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, l, } { n, −h,b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k, } { o, −k, g, −c, b,−f, j, −n, −p, l, −h, d, −a, e, −i, m, } { p, −n, l, −j, h, −f, d, −b,a, −c, e, −g, i, −k, m, −o, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 87, 84,81, 77, 73, 68, 62, 55, 48, 40, 33, 25, 16, 8}

According to another embodiment, the transform core matrices may be:

16-point DST-7:

{ a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p, } { c, f,  i,  l,  o,  o,  l,  i,  f,  c,  0, −c, −f, −i, −l, −o, } { e,  j, o,  m,  h,  c, −b, −g, −l, −p, −k, −f, −a,  d,  i,  n, } { g,  n,  l, e, −b, −i, −p, −j, −c,  d,  k,  o,  h,  a, −f, −m, } { i,  o,  f, −c,−l, −l, −c,  f,  o,  i,  0, −i, −o, −f,  c,  l, } { k,  k,  0, −k, −k, 0,  k,  k,  0, −k, −k,  0,  k,  k,  0, −k, } { m,  g, −f, −n, −a,  l, h, −e, −o, −b,  k,  i, −d, −p, −c,  j, } { o,  c, −l, −f,  i,  i, −f,−l,  c,  o,  0, −o, −c,  l,  f, −i, } { p, −a, −o,  b,  n, −c, −m,  d, l, −e, −k,  f,  j, −g, −i,  h, } { n, −e, −i,  j,  d, −o,  a,  m, −f,−h,  k,  c, −p,  b,  l, −g, } { l, −i, −c,  o, −f, −f,  o, −c, −i,  l, 0, −l,  i,  c, −o,  f, } { j, −m,  c,  g, −p,  f,  d, −n,  i,  a, −k, l, −b, −h,  o, −e, } { h, −p,  i, −a, −g,  o, −j,  b,  f, −n,  k, −c,−e,  m, −l,  d, } { f, −l,  o, −i,  c,  c, −i,  o, −l,  f,  0, −f,  l,−o,  i, −c, } { d, −h,  l, −p,  m, −i,  e, −a, −c,  g, −k,  o, −n,  j,−f,  b, } { b, −d,  f, −h,  j, −l,  n, −p,  o, −m,  k, −i,  g, −e,  c,−a, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={7, 18, 25, 34,40, 48, 54, 61, 68, 74, 77, 81, 86, 86, 88, 88}

16-point DCT-8:

     { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, }      { b, e, h,k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c, h, m, −p, −k,−f, −a, −e, −j, −o, n, i, d, b, g, l, } { d, k, −p, −i, −b, −f, −m, n,g, a, h, o, −l, −e, −c, −j, } { e, n, −k, −b, −h, 0, h, b, k, −n, −e,−e, −n, k, b, h, } { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0, −f,−f, } { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d, } { h,−k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b, } { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a, } { j, −e, −o, a, −n, −f, i,k, −d, −p, b, −m, −g, h, l, −c, } { k, −b, n, h, −e, 0, e, −h, −n, b,−k, −k, b, −n, −h, e, } { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j,−n, d, −g, } { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, l, }{ n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k, } { o, −k, g,−c, b, −f, j, −n, −p, l, −h, d, −a, e, −i, m, } { p, −n, l, −j, h, −f,d, −b, a, −c, e, −g, i, −k, m, −o, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 86, 86,81, 77, 74, 68, 61, 54, 48, 40, 34, 25, 18, 7}

According to another embodiment, the transform core matrices may be:

16-point DST-7:

     { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, }      { c, f, i,l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o, } { e, j, o, m, h, c, −b,−g, −l, −p, −k, −f, −a, d, i, n, } { g, n, l, e, −b, −i, −p, −j, −c, d,k, o, h, a, −f, −m, } { i, o, f, −c, −l, −l, −c, f, o, i, 0, −i, −o, −f,c, l, } { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k, k, 0, −k, } { m, g,−f, −n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c, j, } { o, c, −l, −f, i,i, −f, −l, c, o, 0, −o, −c, l, f, −i, } { p, −a, −o, b, n, −c, −m, d, l,−e, −k, f, j, −g, −i, h, } { n, −e, −i, j, d, −o, a, m, −f, −h, k, c,−p, b, l, −g, } { l, −i, −c, o, −f, −f, o, −c, −i, l, 0, −l, i, c, −o,f, } { j, −m, c, g, −p, f, d, −n, i, a, −k, l, −b, −h, o, −e, } { h, −p,i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l, d, } { f, −l, o, −i, c, c,−i, o, −l, f, 0, −f, l, −o, i, −c, } { d, −h, l, −p, m, −i, e, −a, −c,g, −k, o, −n, j, −f, b, } { b, −d, f, −h, j, −l, n, −p, o, −m, k, −i, g,−e, c, −a, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={7, 17, 25, 33,40, 48, 55, 62, 68, 74, 77, 81, 85, 87, 88, 88}16-point DCT-8:

     { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, }      { b, e, h,k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c, h, m, −p, −k,−f, −a, −e, −j, −o, n, i, d, b, g, l, } { d, k, −p, −i, −b, −f, −m, n,g, a, h, o, −l, −e, −c, −j, } { e, n, −k, −b, −h, 0, h, b, k, −n, −e,−e, −n, k, b, h, } { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0, −f,−f, } { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d, } { h,−k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b, } { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a, } { j, −e, −o, a, −n, −f, i,k, −d, −p, b, −m, −g, h, l, −c, } { k, −b, n, h, −e, 0, e, −h, −n, b,−k, −k, b, −n, −h, e, } { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j,−n, d, −g, } { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i, }{ n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k, } { o, −k, g,−c, b, −f, j, −n, −p, l, −h, d, −a, e, −i, m, } { p, −n, l, −j, h, −f,d, −b, a, −c, e, −g, i, −k, m, −o, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 87, 85,81, 77, 74, 68, 62, 55, 48, 40, 33, 25, 17, 7}

According to another embodiment, the transform core matrices may be:

16-point DST-7:

     { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, }      { c, f, i,l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o, } { e, j, o, m, h, c, −b,−g, −l, −p, −k, −f, −a, d, i, n, } { g, n, l, e, −b, −i, −p, −j, −c, d,k, o, h, a, −f, −m, } { i, o, f, −c, −l, −l, −c, f, o, i, 0, −i, −o, c,l, l } { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k, k, 0, −k, } { m, g,−f, −n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c, j, } { o, c, −l, −f, i,i, −f, −l, c, o, 0, −o, −c, l, f, −i, } { p, −a, −o, b, n, −c, −m, d, l,−e, −k, f, j, −g, −i, h, } { n, −e, −i, j, d, −o, a, m, −f, −h, k, c,−p, b, l, −g, } { l, −i, −c, o, −f, −f, o, −c, −i, l, 0, −l, i, c, −o,f, } { j, −m, c, g, −p, f, d, −n, i, a, −k, l, −b, −h, o, −e, } { h, −p,i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l, d, } { f, −l, o, −i, c, c,−i, o, −l, f, 0, −f, l, −o, i, −c, } { d, −h, l, −p, m, −i, e, −a, −c,g, −k, o, −n, j, −f, b, } { b, −d, f, −h, j, −l, n, −p, o, −m, k, −i, g,−e, c, −a, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={7, 16, 25, 33,40, 48, 55, 62, 68, 74, 77, 81, 84, 87, 88, 88}16-point DCT-8:

     { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, }      { b, e, h,k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n, } { c, h, m, −p, −k,−f, −a, −e, −j, −o, n, i, d, b, g, l, } { d, k, −p, −i, −b, −f, −m, n,g, a, h, o, −l, −e, −c, −j, } { e, n, −k, −b, −h, 0, h, b, k, −n, −e,−e, −n, k, b, h, } { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0, −f,−f, } { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d, } { h,−k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b, } { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a, } { j, −e, −o, a, −n, −f, i,k, −d, −p, b, −m, −g, h, l, −c, } { k, −b, n, h, −e, 0, e, −h, −n, b,−k, −k, b, −n, −h, e, } { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j,−n, d, −g, } { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i, }{ n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k, } { o, −k, g,−c, b, −f, j, −n, −p, l, −h, d, −a, e, −i, m, } { p, −n, l, −j, h, −f,d, −b, a, −c, e, −g, i, −k, m, −o, }where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 87, 84,81, 77, 74, 68, 62, 55, 48, 40, 33, 25, 16, 7}

FIG. 6 is a flowchart illustrating a method (600) of decoding orencoding of a video sequence, according to an embodiment. In someimplementations, one or more process blocks of FIG. 6 may be performedby the decoder (310). In some implementations, one or more processblocks of FIG. 6 may be performed by another device or a group ofdevices separate from or including the decoder (310), such as theencoder (303).

Referring to FIG. 6 , in a first block (610), the method (600) includesreceiving information regarding a video sequence for encoding ordecoding.

In a second block (620), the method (600) includes determining, for theencoding or decoding of the video sequence, whether to use a firsttransform core matrix that is of a first size type or a second transformcore matrix that is of a second size type.

In a third block (630), the method (600) includes based on thedetermining, transmitting information that causes the video sequence tobe encoded or decoded using the determined first transform core matrixor second transform core matrix.

Although FIG. 6 shows example blocks of methods (600), in someimplementations, the method (600) may include additional blocks, fewerblocks, different blocks, or differently arranged blocks than thosedepicted in FIG. 6 . Additionally, or alternatively, two or more of theblocks of the method (600) may be performed in parallel.

Further, the proposed method may be implemented by processing circuitry(e.g., one or more processors or one or more integrated circuits). In anexample, the one or more processors execute a program that is stored ina non-transitory computer-readable medium to perform one or more of theproposed methods.

FIG. 7 illustrates example transform core matrices, according to anembodiment. For example, transform core matrix 701 illustrates atransform core matrix of 16-point discrete sine transform (DST)-7, andtransform core matrix 702 illustrates a transform core matrix ofdiscrete cosine transform (DCT)-8.

FIG. 8 is a simplified block diagram of an apparatus (800) for decodingor encoding of a video sequence, according to an embodiment.

Referring to FIG. 8 , the apparatus (800) includes receiving code (810),determining code (820), and transmitting code (830).

The determining code (810) is configured to cause the at least oneprocessor to receive information regarding a video sequence for encodingor decoding.

The determining code (820) is configured to cause the at least oneprocessor to determine, for the encoding or decoding of the videosequence, whether to use a first transform core matrix that is of afirst size type or a second transform core matrix that is of a secondsize type.

The transmitting code (830) is configured to cause the at least oneprocessor to, based on the determining, transmit information that causesthe video sequence to be encoded or decoded using the determined firsttransform core matrix or second transform core matrix.

The techniques described above, can be implemented as computer softwareusing computer-readable instructions and physically stored in one ormore computer-readable media.

FIG. 9 is a diagram of a computer system (900) suitable for implementingembodiments.

The computer software can be coded using any suitable machine code orcomputer language, that may be subject to assembly, compilation,linking, or like mechanisms to create code comprising instructions thatcan be executed directly, or through interpretation, micro-codeexecution, and the like, by computer central processing units (CPUs),Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers orcomponents thereof, including, for example, personal computers, tabletcomputers, servers, smartphones, gaming devices, internet of thingsdevices, and the like.

The components shown in FIG. 9 for computer system (900) are exemplaryin nature and are not intended to suggest any limitation as to the scopeof use or functionality of the computer software implementingembodiments. Neither should the configuration of components beinterpreted as having any dependency or requirement relating to any oneor combination of components illustrated in the exemplary embodiment ofa computer system (900).

Computer system (900) may include certain human interface input devices.Such a human interface input device may be responsive to input by one ormore human users through, for example, tactile input (such as:keystrokes, swipes, data glove movements), audio input (such as: voice,clapping), visual input (such as: gestures), olfactory input (notdepicted). The human interface devices can also be used to capturecertain media not necessarily directly related to conscious input by ahuman, such as audio (such as: speech, music, ambient sound), images(such as: scanned images, photographic images obtain from a still imagecamera), video (such as two-dimensional video, three-dimensional videoincluding stereoscopic video).

Input human interface devices may include one or more of (only one ofeach depicted): keyboard (901), mouse (902), trackpad (903), touchscreen (910), data-glove (904), joystick (905), microphone (906),scanner (907), camera (908).

Computer system (900) may also include certain human interface outputdevices. Such human interface output devices may be stimulating thesenses of one or more human users through, for example, tactile output,sound, light, and smell/taste. Such human interface output devices mayinclude tactile output devices (for example tactile feedback by thetouch-screen (910), data-glove (904), or joystick (905), but there canalso be tactile feedback devices that do not serve as input devices),audio output devices (such as: speakers (909), headphones (notdepicted)), visual output devices (such as screens (910) to includecathode ray tube (CRT) screens, liquid-crystal display (LCD) screens,plasma screens, organic light-emitting diode (OLED) screens, each withor without touch-screen input capability, each with or without tactilefeedback capability−some of which may be capable to output twodimensional visual output or more than three dimensional output throughmeans such as stereographic output; virtual-reality glasses (notdepicted), holographic displays and smoke tanks (not depicted)), andprinters (not depicted).

Computer system (900) can also include human accessible storage devicesand their associated media such as optical media including CD/DVD ROM/RW(920) with CD/DVD or the like media (921), thumb-drive (922), removablehard drive or solid state drive (923), legacy magnetic media such astape and floppy disc (not depicted), specialized ROM/ASIC/PLD baseddevices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computerreadable media” as used in connection with the presently disclosedsubject matter does not encompass transmission media, carrier waves, orother transitory signals.

Computer system (900) can also include interface(s) to one or morecommunication networks. Networks can for example be wireless, wireline,optical. Networks can further be local, wide-area, metropolitan,vehicular and industrial, real-time, delay-tolerant, and so on. Examplesof networks include local area networks such as Ethernet, wireless LANs,cellular networks to include global systems for mobile communications(GSM), third generation (3G), fourth generation (4G), fifth generation(5G), Long-Term Evolution (LTE), and the like, TV wireline or wirelesswide area digital networks to include cable TV, satellite TV, andterrestrial broadcast TV, vehicular and industrial to include CANBus,and so forth. Certain networks commonly require external networkinterface adapters that attached to certain general purpose data portsor peripheral buses ((949)) (such as, for example universal serial bus(USB) ports of the computer system (900); others are commonly integratedinto the core of the computer system (900) by attachment to a system busas described below (for example Ethernet interface into a PC computersystem or cellular network interface into a smartphone computer system).Using any of these networks, computer system (900) can communicate withother entities. Such communication can be uni-directional, receive only(for example, broadcast TV), uni-directional send-only (for exampleCANbus to certain CANbus devices), or bi-directional, for example toother computer systems using local or wide area digital networks.Certain protocols and protocol stacks can be used on each of thosenetworks and network interfaces as described above.

Aforementioned human interface devices, human-accessible storagedevices, and network interfaces can be attached to a core (940) of thecomputer system (900).

The core (940) can include one or more Central Processing Units (CPU)(941), Graphics Processing Units (GPU) (942), specialized programmableprocessing units in the form of Field Programmable Gate Areas (FPGA)(943), hardware accelerators (944) for certain tasks, and so forth.These devices, along with Read-only memory (ROM) (945), Random-accessmemory (RAM) (946), internal mass storage such as internal non-useraccessible hard drives, solid-state drives (SSDs), and the like (947),may be connected through a system bus (948). In some computer systems,the system bus (948) can be accessible in the form of one or morephysical plugs to enable extensions by additional CPUs, GPU, and thelike. The peripheral devices can be attached either directly to thecore's system bus (948), or through a peripheral bus (949).Architectures for a peripheral bus include peripheral componentinterconnect (PCI), USB, and the like.

CPUs (941), GPUs (942), FPGAs (943), and accelerators (944) can executecertain instructions that, in combination, can make up theaforementioned computer code. That computer code can be stored in ROM(945) or RAM (946). Transitional data can also be stored in RAM (946),whereas permanent data can be stored for example, in the internal massstorage (947). Fast storage and retrieve to any of the memory devicescan be enabled through the use of cache memory, that can be closelyassociated with one or more CPU (941), GPU (942), mass storage (947),ROM (945), RAM (946), and the like.

The computer readable media can have computer code thereon forperforming various computer-implemented operations. The media andcomputer code can be those specially designed and constructed for thepurposes of embodiments, or they can be of the kind well known andavailable to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system havingarchitecture (900), and specifically the core (940) can providefunctionality as a result of processor(s) (including CPUs, GPUs, FPGA,accelerators, and the like) executing software embodied in one or moretangible, computer-readable media. Such computer-readable media can bemedia associated with user-accessible mass storage as introduced above,as well as certain storage of the core (940) that are of non-transitorynature, such as core-internal mass storage (947) or ROM (945). Thesoftware implementing various embodiments can be stored in such devicesand executed by core (940). A computer-readable medium can include oneor more memory devices or chips, according to particular needs. Thesoftware can cause the core (940) and specifically the processorstherein (including CPU, GPU, FPGA, and the like) to execute particularprocesses or particular parts of particular processes described herein,including defining data structures stored in RAM (946) and modifyingsuch data structures according to the processes defined by the software.In addition or as an alternative, the computer system can providefunctionality as a result of logic hardwired or otherwise embodied in acircuit (for example: accelerator (944)), which can operate in place ofor together with software to execute particular processes or particularparts of particular processes described herein. Reference to softwarecan encompass logic, and vice versa, where appropriate. Reference to acomputer-readable media can encompass a circuit (such as an integratedcircuit (IC)) storing software for execution, a circuit embodying logicfor execution, or both, where appropriate. Embodiments encompass anysuitable combination of hardware and software.

While this disclosure has described several exemplary embodiments, thereare alterations, permutations, and various substitute equivalents, whichfall within the scope of the disclosure. It will thus be appreciatedthat those skilled in the art will be able to devise numerous systemsand methods which, although not explicitly shown or described herein,embody the principles of the disclosure and are thus within the spiritand scope thereof.

The invention claimed is:
 1. A method of decoding, the method beingperformed by at least one processor, and the method comprising:receiving information regarding a video sequence for decoding, whereinthe video sequence information comprises one or more symbolscorresponding to control information to manage operation of one or moredevices, the control information comprising memory addresses ofprediction samples corresponding to a reference picture associated withthe video sequence, the prediction samples being configured to becontrolled by motion vectors; determining, for the decoding of the videosequence, whether to use a first transform core matrix that is of afirst size type or a second transform core matrix that is of a secondsize type, wherein the first transform core matrix is one of a 16 pointdiscrete sine transform (DST)-7 or a 32 point DST-7, wherein the secondtransform core matrix is one of a 16 point discrete cosine transform(DCT)-8 or a 32 point DCT-8, wherein the 16-point DST-7 is constructedusing following matrix:   { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o,p,} { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o,} { e, j, o,m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g, n, l, e, −b, −i, −p,−j, −c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l, −l, −c, f, o, i, 0,−i, −o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k, k, 0,−k,} { m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c, j,} { o, c,−l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} { p, −a, −o, b, n, −c,−m, d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j, d, −o, a, m, −f, −h,k, c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c, −i, l, 0, −l, i, c,−o, f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l, −b, −h, o, −e,} { h,−p, i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l, d,} { f, −l, o, −i, c,c, −i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h, l, −p, m, −i, e, −a, −c,g, −k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l, n, −p, o, −m, k, −i, g,−e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={7, 18, 25, 34,40, 48, 54, 61, 68, 74, 77, 81, 86, 86, 88, 88}; based on thedetermining, transmitting information that causes the video sequence tobe decoded by the one or more devices using the determined firsttransform core matrix or second transform core matrix.
 2. The method ofclaim 1, wherein the first transform core matrix is a 32-point DST-7that is constructed using the following matrix: { a, b, c, d, e, f, g,h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E,F,} { c, f, i, l, o, r, u, x, A, D, F, C, z, w, t, q, n, k, h, e, b, −a,−d, −g, −j, −m, −p, −s, −v, −y, −B, −E,} { e, j, o, t, y, D, D, y, t, o,j, e, 0, −e, −j, −o, −t, −y, −D, −D, −y, −t, −o, −j, −e, 0, e, j, o, t,y, D,} { g, n, u, B, D, w, p, i, b, −e, −l, −s, −z, −F, −y, −r, −k, −d,c, j, q, x, E, A, t, m, f, −a, −h, −o, −v, −C,} { i, r, A, C, t, k, b,−g, −p, −y, −E, −v, −m, −d, e, n, w, F, x, o, f, −c, −l, −u, −D, −z, −q,−h, a, j, s, B,} { k, v, F, u, j, −a, −l, −w, −E, −t, −i, b, m, x, D, s,h, −c, −n, −y, −C, −r, −g, d, o, z, B, q, f, −e, −p, −A,} { m, z, z, m,0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0,−m, −z, −z, −m, 0, m, z,} { o, D, t, e, −j, −y, −y, −j, e, t, D, o, 0,−o, −D, −t, −e, j, y, y, j, −e, −t, −D, −o, 0, o, D, t, e, −j, −y,} { q,E, n, −c, −t, −B, −k, f, w, y, h, −i, −z, −v, −e, l, C, s, b, −o, −F,−p, a, r, D, m, −d, −u, −A, −j, g, x,} { s, A, h, −k, −D, −p, c, v, x,e, −n, −F, −m, f, y, u, b, −q, −C, −j, i, B, r, −a, −t, −z, −g, l, E, o,−d, −w,} { u, w, b, −s, −y, −d, q, A, f, −o, −C, −h, m, E, j, −k, −F,−l, i, D, n, −g, −B, −p, e, z, r, −c, −x, −t, a, v,} { w, s, −d, −A, −o,h, E, k, −l, −D, −g, p, z, c, −t, −v, a, x, r, −e, −B, −n, i, F, j, −m,−C, −f, q, y, b, −u,} { y, o, −j, −D, −c, t, t, −c, −D, −j, o, y, 0, −y,−o, j, D, c, −t, −t, c, D, j, −o, −y, 0, y, o, −j, −D, −c, t,} { A, k,−p, −v, e, F, f, −u, −q, j, B, a, −z, −l, o, w, −d, −E, −g, t, r, −i,−C, −b, y, m, −n, −x, c, D, h, −s,} { C, g, −v, −n, o, u, −h, −B, a, D,f, −w, −m, p, t, −i, −A, b, E, c, −x, −l, q, s, −j, −z, c, F, d, −y, −k,r,} { E, c, −B, −f, y, i, −v, −l, s, o, −p, −r, m, u, −j, −x, g, A, −d,−D, a, F, b, −C, −e, z, h, −w, −k, t, n, −q,} { F, −a, −E, b, D, −c, −C,d, B, −e, −A, f, z, −g, −y, h, x, −i, −w, j, v, −k, −u, l, t, −m, −s, n,r, −o, −q, p,} { D, −e, −y, j, t, −o, −o, t, j, −y, −e, D, 0, −D, e, y,−j, −t, o, o, −t, −j, y, e, −D, 0, D, −e, −y, j, t, −o,} { B, −i, −s, r,j, −A, −a, C, −h, −t, q, k, −z, −b, D, −g, −u, p, l, −y, −c, E, −f, −v,o, m, −x, −d, F, −e, −w, n,} { z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m,−m, z, 0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m,} {x, −q, −g, E, −j, −n, A, −c, −u, t, d, −B, m, k, −D, f, r, −w, −a, y,−p, −h, F, −i, −o, z, −b, −v, s, c, −C, l,} { v, −u, −a, w, −t, −b, x,−s, −c, y, −r, −d, z, −q, −c, A, −p, −f, B, −o, −g, C, −n, −h, D, −m,−i, E, −l, −j, F, −k} { t, −y, c, o, −D, j, j, −D, o, e, −y, t, 0, −t,y, −e, −o, D, −j, −j, D, −o, −e, y, −t, 0, t, −y, c, o, −D, j,} { r, −C,k, g, −y, v, −d, −n, F, −o, −c, u, −z, h, j, −B, s, −a, −q, D, −l, −f,x, −w, e, m, −E, p, b, −t, A, −i,} { p, −F, q, −a, −o, E, −r, b, n, −D,s, −c, −m, C, −t, d, l, −B, u, −e, −k, A, −v, f, j, −z, w, −g, −i, y,−x, h,} { n, −B, w, −i, −e, s, −F, r, −d, −j, x, −A, m, a, −o, C, −v, h,f, −t, E, −q, c, k, −y, z, −l, −b, p, −D, u, −g,} { l, −x, C, −q, e, g,−s, E, −v, j, b, −n, z, −A, o, −c, −i, u, −F, t, −h, −d, p, −B, y, −m,a, k, −w, D, −r, f,} { j, −t, D, −y, o, −c, −e, o, −y, D, −t, j, 0, −j,t, −D, y, −o, c, c, −o, y, −D, t, −j, 0, j, −t, D, −y, o, −e,} { h, −p,x, −F, y, −q, i, −a, −g, o, −w, E, −z, r, −j, b, f, −n, v, −D, A, −s, k,−c, −c, m, −u, C, −B, t, −l, d,} { f, −l, r, −x, D, −C, w, −q, k, −c,−a, g, −m, s, −y, E, −B, v, −p, j, −d, −b, h, −n, t, −z, F, −A, u, −o,i, −c,} { d, −h, l, −p, t, −x, B, −F, C, −y, u, −q, m, −i, c, −a, −c, g,−k, o, −s, w, −A, E, −D, z, −v, r, −n, j, −f, b,} { b, −d, f, −h, j, −l,n, −p, r, −t, v, −x, z, −B, D, −F, E, −C, A, −y, w, −u, s, −q, o, −m, k,−i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u,v, w, x, y, z, A, B, C, D, E, F}={4, 9, 13, 17, 21, 26, 30, 34, 38, 42,46, 50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 87,88, 89, 90, 90}, and wherein the second transform core matrix is a32-point DCT-8 that is constructed using following matrix: { a, b, c, d,e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B,C, D, E, F,} { b, c, h, k, n, q, t, w, z, C, F, −E, −B, −y, −v, −s, −p,−m, −j, −g, −d, −a, −c, −f, −i, −l, −o, −r, −u, −x, −A, −D,} { c, h, m,r, w, B, 0, −B, −w, −r, −m, −h, −c, −c, −h, −m, −r, −w, −B, 0, B, w, r,m, h, c, c, h, m, r, w, B,} { d, k, r, y, F, −A, −t, −m, −f, −b, −i, −p,−w, −D, C, v, o, h, a, g, n, u, B, −E, −x, −q, −j, −c, −e, −l, −s, −z,}{ e, n, w, F, −y, −p, −g, −c, −l, −u, −D, A, r, i, a, j, s, B, −C, −t,−k, −b, −h, −q, −z, E, v, m, d, f, o, x,} { f, q, B, −A, −p, −e, −g, −r,−C, z, o, d, h, s, D, −y, −n, −c, −i, −t, −E, x, m, b, j, u, F, −w, −l,−a, −k, −v,} { g, t, 0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g,−t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t,} { h, w, −B, −m,−c, −r, 0, r, c, m, B, −w, −h, −h, −w, B, m, c, r, 0, −r, −c, −m, −B, w,h, h, w, −B, −m, −c, −r,} { i, z, −w, −f, −l, −C, t, c, o, F, −q, −a,−r, E, n, d, u, −B, −k, −g, −x, y, h, j, A, −v, −c, −m, −D, s, b, p,} {j, C, −r, −b, −u, z, g, m, F −o, −c, −x, w, d, p, −E, −l, −h, −A, t, a,s, −B, −i, −k, −D, q, c, v, −y, −f, −n,} { k, vF, −m, −i, −D, o, g, B,−q, −e, −z, s, c, x, −u, −a, −v, w, b, t, −y, −d, −r, A, f, p, −C, −b,−n, E, j, l,} { l, −E, −h, −p, A, d, t, −w, −a, −x, s, e, B, −o, −i, −F,k, m, −D, −g, −q, z, c, u, −v, −b, −y, r, f, C, −n, −j,} { m, −B, −c,−w, r, h, 0, −h, −r, w, c, B, −m, −m, B, c, w, −r, −h, 0, h, r, −w, −c,−B, m, m, −B, −c, −w, r, h,} { n, −y, −c, −D, i, s, −t, −h, E, d, x, −o,−m, z, b, C, −j, −r, u, g, −F, −e, −w, p, l, −A, −a, −B, k, q, −v, −f,}{ o, −v, −h, C, a, D, −g, −w, n, p, −u, −i, B, b, E, −f, −x, m, q, −t,−j, A, c, F, −e, −y, l, r, −s, −k, z, d,} { p, −s, −m, v, j, −y, −g, B,d, −E, −a, −F, c, C, −f, −z, i, w, −l, −t, o, q, −r, −n, u, k, −x, −h,A, e, −D, −b,} { q, −p, −r, o, s, −n, −t, m, u, −l, −v, k, w, −j, −x, i,y, −h, −z, g, A, −f, −B, e, C, −d, −D, c, E, −b, −F, a,} { r, −m, −w, h,B, −c, 0, c, −B, −h, w, m, −r, −r, m, w, −h, −B, c, 0, −c, B, h, −w, −m,r, r, −m, −w, h, B, −c,} { s, −j, −B, a, −C, −i, t, r, −k, −A, b, −D,−h, u, q, −l, −z, c, −E, −g, v, p, −m, −y, d, −F, −f, w, o, −n, −x, e,}{ t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t, t,−g, 0, g, −t, −t, g, 0, −g, t, t, −g,} { u, −d, B, n, −k, −E, g, −r, −x,a, −y, −q, h, −F, −j, o, A, −c, v, t, −c, C, m, −l, −D, f, −s, −w, b,−z, −p, i,} { v, −a, w, u, −b, x, t, −c, y, s, −d, z, r, −c, A, q, −f,B, p, −g, C, o, −h, D, n, −i, E, m, −j, F, l, −k,} { w, −c, r, B, −h, m,0, −m, h, −B, −r, c, −w, −w, c, −r, −B, h, −m, 0, m, −h, B, r, −c, w, w,−c, r, B, −h, m,} { x, −f, m, −E, −q, b, −t, −B, j, −i, A, u, −c, p, F,−n, e, −w, −y, g, −l, D, r, −a, s, C, −k, h, −z, −v, d, −o,} { y, −i, h,−x, −z, j, −g, w, A, −k, f, −v, −B, l, −e, u, C, −m, d, −t, −D, n, −c,s, E, −o, b, −r, −F, p, −a, q,} { z, −l, c, −q, E, u, −g, h, −v, −D, p,−b, m, −A, −y, k, −d, r, −F, −t, f, −i, w, C, −o, a, −n, B, x, −j, e,−s,} { A, −o, c, −j, v, F, −t, h, −e, q, −C, −y, m, −a, l, −x, −D, r,−f, g, −s, E, w, −k, b, −n, z, B, −p, d, −i, u,} { B, −r, h, −c, m, −w,0, w, −m, c, −h, r, −B, −B, r, −h, c, −m, w, 0, −w, m, −c, h, −r, B, B,−r, h, −c, m, −w,} { C, −u, m, −c, d, −l, t, −B, −D, v, −n, f, −c, k,−s, A, E, −w, o, −g, b, −j, r, −z, −F, x, −p, h, −a, i, −q, y,} { D, −x,r, −l, f, −a, g, −m, s, −y, E, C, −w, q, −k, c, −b, h, −n, t, −z, F, B,−v, p, −j, d, −c, i, −o, u, −A,} { E, −A, w, −s, o, −k, g, −c, b, −f, j,−n, r, −v, z, −D, −F, B, −x, t, −p, l, −h, d, −a, e, −i, m, −q, u, −y,C,} { F, −D, B, −z, x, −v, t, −r, p, −n, l, −j, h, −f, d, −b, a, −c, e,−g, i, −k, m, −o, q, −s, u, −w, y, −A, C, −E,},

wherein{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u,v, w, x, y, z, A, B, C, D, E, F}={90, 90, 89, 88, 87, 86, 85, 84, 82,80, 78, 77, 74, 72, 68, 66, 63, 60, 56, 53, 50, 46, 42, 38, 34, 30, 26,21, 17, 13, 9, 4}.
 3. The method of claim 1, wherein the first transformcore matrix is a wherein the second transform core matrix is a 16-pointDCT-8 that is constructed using following matrix:   { a, b, c, d, e, f,g, h, i, j, k, l, m, n, o, p,} { b, e, h, k, n, 0, −n, −k, −h, −e, −b,−b, −e, −h, −k, −n,} { c, h, m, −p, −k, −f, −a, −e, −j, −o, n, i, d, b,g, l,} { d, k, −p, −i, −b, −f, −m, n, g, a, h, o, −l, −e, −c, −j,} { e,n, −k, −b, −h, 0, h, b, k, −n, −e, −e, −n, k, b, h,} { f, 0, −f, −f, 0,f, f, 0, −f, −f, 0, f, f, 0, −f, −f,} { g, −n, −a, −m, h, f, −o, −b, −l,i, e, −p, −c, −k, j, d,} { h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k,e, −n, −b,} { i, −h, −j, g, k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} {j, −e, −o, a, −n, −f, i, k, −d, −p, b, −m, −g, h, l, −c,} { k, −b, n, h,−e, 0, e, −h, −n, b, −k, −k, b, −n, −h, e,} { l, −b, i, o, −e, f, −p,−h, c, −m, −k, a, −j, −n, d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g,b, −j, −p, h, −a, i,} { n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b,e, −k,} { o, −k, g, −c, b, −f, j, −n, −p, l, −h, d, −a, e, −i, m,} { p,−n, l, −j, h, −f, d, −b, a, −c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 86,86, 81, 77, 74, 68, 61, 54, 48, 40, 34, 25, 18, 7}.
 4. The method ofclaim 1, wherein the first transform core matrix is a 16-point DST-7that is constructed using following matrix:   { a, b, c, d, e, f, g, h,i, j, k, l, m, n, o, p,} { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i,−l, −o,} { e, j, o, m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g,n, l, e, −b, −i, −p, −j, −c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l,−l, −c, f, o, i, 0, −i, −o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0,−k, −k, 0, k, k, 0, −k,} { m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d,−p, −c, j,} { o, c, −l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} {p, −a, −o, b, n, −c, −m, d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j,d, −o, a, m, −f, −h, k, c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c,−i, l, 0, −l, i, c, −o, f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l,−b, −h, o, −e,} { h, −p, i, −a, −g, o, −j, b, f, −n, k, −c, −c, m, −l,d,} { f, −l, o, −i, c, c, −i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h,l, −p, m, −i, e, −a, −c, g, −k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l,n, −p, o, −m, k, −i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={9, 17, 25, 33,41, 48, 55, 61, 68, 72, 77, 81, 85, 86, 88, 89}, and wherein the secondtransform core matrix is a 16-point DCT-8 that is constructed usingfollowing matrix:   { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,} {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,} { c, h, m,−p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, l,} { d, k, −p, −i, −b, −f,−m, n, g, a, h, o, −l, −e, −c, −j,} { e, n, −k, −b, −h, 0, h, b, k, −n,−e, −e, −n, k, b, h,} { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0,−f, −f,} { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d,} {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,} { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} { j, −e, −o, a, −n, −f, i, k,−d, −p, b, −m, −g, h, l, −c,} { k, −b, n, h, −e, 0, e, −h, −n, b, −k,−k, b, −n, −h, e,} { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n,d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,} { n,−h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,} { o, −k, g, −c, b,−f, j, −n, −p, l, −h, d, −a, e, −i, m,} { p, −n, l, −j, h, −f, d, −b, a,−c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p}={89, 88, 86, 85,81, 77, 72, 68, 61, 55, 48, 41, 33, 25, 17, 9}.
 5. The method of claim1, wherein the first transform core matrix is a 16-point DST-7 that isconstructed using following matrix:   { a, b, c, d, e, f, g, h, i, j, k,l, m, n, o, p,} { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o,}{ e, j, o, m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g, n, l, e,−b, −i, −p, −j, −c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l, −l, −c,f, o, i, 0, −i, −o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0,k, k, 0, −k,} { m, g, −f, −n, −a, l, h, −c, −o, −b, k, i, −d, −p, −c,j,} { o, c, −l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} { p, −a,−o, b, n, −c, −m, d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j, d, −o,a, m, −f, −h, k, c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c, −i, l,0, −l, i, c, −o, f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l, −b, −h,o, −e,} { h, −p, i, −a, −g, o, −j, b, f, −n, k, −c, −c, m, −l, d,} { f,−l, o, −i, c, c, −i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h, l, −p, m,−i, e, −a, −c, g, −k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l, n, −p, o,−m, k, −i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={8, 17, 25, 33,40, 48, 55, 62, 68, 73, 77, 81, 85, 87, 88, 88}, and wherein the secondtransform core matrix is a 16-point DCT-8 that is constructed usingfollowing matrix:   { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,} {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,} { c, h, m,−p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, l,} { d, k, −p, −i, −b, −f,−m, n, g, a, h, o, −l, −e, −c, −j,} { e, n, −k, −b, −h, 0, h, b, k, −n,−e, −e, −n, k, b, h,} { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0,−f, −f,} { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d,} {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,} { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} { j, −e, −o, a, −n, −f, i, k,−d, −p, b, −m, −g, h, l, −c,} { k, −b, n, h, −e, 0, e, −h, −n, b, −k,−k, b, −n, −h, e,} { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n,d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,} { n,−h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,} { o, −k, g, −c, b,−f, j, −n, −p, l, −h, d, −a, e, −i, m,} { p, −n, l, −j, h, −f, d, −b, a,−c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 87,85, 81, 77, 73, 68, 62, 55, 48, 40, 33, 25, 17, 8}.
 6. The method ofclaim 1, wherein the control information comprises at least one of:Supplementary Enhancement Information (SEI) messages and Video UsabilityInformation (VUI) parameter set fragments.
 7. The method of claim 1,wherein the determining of whether to use the first transform corematrix that is of the first size type or the second transform corematrix that is of the second size type is based on a flag signaled usingtwo bins to identify a horizontal transform and a vertical transform. 8.An apparatus for decoding of a video sequence, the apparatus comprising:at least one memory configured to store computer program code; and atleast one processor configured to access the at least one memory andoperate according to the computer program code, the computer programcode comprising: receiving code configured to cause the at least oneprocessor to receive information regarding a video sequence fordecoding, wherein the video sequence information comprises one or moresymbols corresponding to control information to manage operation of oneor more devices, the control information comprising memory addresses ofprediction samples corresponding to a reference picture associated withthe video sequence, the prediction samples being configured to becontrolled by motion vectors; determining code configured to cause theat least one processor to determine, for the decoding of the videosequence, whether to use a first transform core matrix that is of afirst size type or a second transform core matrix that is of a secondsize type, wherein the first transform core matrix is one of a 16 pointdiscrete sine transform (DST)-7 or a 32 point DST-7, wherein the secondtransform core matrix is one of a 16 point discrete cosine transform(DCT)-8 or a 32 point DCT-8, wherein the 16-point DST-7 is constructedusing following matrix: { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o,p, } { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o, } { e, j, o,m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n, } { g, n, l, e, −b, −i,−p, −j, − c, d, k, o, h, a, −f, −m, } { i, o, f, −c, −l, −l, −c, f, o,i, 0, −i, −o, −f, c, l, } { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k,k, 0, −k, } { m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c, i, }{ o, c, −l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i, } { p, −a, −o,b, n, −c, −m, d, l, −e, −k, f, j, − g, −i, h, } { n, −e, −i, j, d, − o,a, m, −f, −h, k, c, −p, b, l, −g, } { l, −i, −c, o, −f, −f, o, −c, −i,l, 0, −l, i, c, −o, f, } { j, − m, c, g, − p, f, d, −n, i, a, −k, l, −b,−h, o, −e, } { h, −p, i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l, d, }{ f, −l, o, −i, c, c, −i, o, −l, f, 0, −f, l, −o, i, −c, } { d, −h, l,−p, m, −i, e, −a, −c, g, − k, o, −n, j, −f, b, } { b, −d, f, −h, j, − l,n, − p, o, −m, k, −i, g, −e, c, −a, },

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={7, 18, 25, 34,40, 48, 54, 61, 68, 74, 77, 81, 86, 86, 88, 88}; and transmitting codeconfigured to cause the at least one processor to, based on thedetermining, transmit information that causes the video sequence to bedecoded by the one or more devices using the determined first transformcore matrix or second transform core matrix.
 9. The apparatus of claim8, wherein the first transform core matrix is a 32-point DST-7 that isconstructed using the following matrix: { a, b, c, d, e, f, g, h, i, j,k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F,} { c,f, i, l, o, r, u, x, A, D, F, C, z, w, t, q, n, k, h, e, b, −a, −d, −g,−j, −m, −p, −s, −v, −y, −B, −E,} { e, j, o, t, y, D, D, y, t, o, j, e,0, −e, −j, −o, −t, −y, −D, −D, −y, −t, −o, −j, −e, 0, e, j, o, t, y, D,}{ g, n, u, B, D, w, p, i, b, −e, −l, −s, −z, −F, −y, −r, −k, −d, c, j,q, x, E, A, t, m, f, −a, −h, −o, −v, −C,} { i, r, A, C, t, k, b, −g, −p,−y, −E, −v, −m, −d, e, n, w, F, x, o, f, −c, −l, −u, −D, −z, −q, −h, a,j, s, B,} { k, v, F, u, j, −a, −l, −w, −E, −t, −i, b, m, x, D, s, h, −c,−n, −y, −C, −r, −g, d, o, z, B, q, f, −e, −p, −A,} { m, z, z, m, 0, −m,−z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z,−z, −m, 0, m, z,} { o, D, t, e, −j, −y, −y, −j, e, t, D, o, 0, −o, −D,−t, −e, j, y, y, j, −e, −t, −D, −o, 0, o, D, t, e, −j, −y,} { q, E, n,−c, −t, −B, −k, f, w, y, h, −i, −z, −v, −e, l, C, s, b, −o, −F, −p, a,r, D, m, −d, −u, −A, −j, g, x,} { s, A, h, −k, −D, −p, c, v, x, e, −n,−F, −m, f, y, u, b, −q, −C, −j, i, B, r, −a, −t, −z, −g, l, E, o, −d,−w,} { u, w, b, −s, −y, −d, q, A, f, −o, −C, −h, m, E, j, −k, −F, −l, i,D, n, −g, −B, −p, e, z, r, −c, −x, −t, a, v,} { w, s, −d, −A, −o, h, E,k, −l, −D, −g, p, z, c, −t, −v, a, x, r, −e, −B, −n, i, F, j, −m, −C,−f, q, y, b, −u,} { y, o, −j, −D, −e, t, t, −e, −D, −j, o, y, 0, −y, −o,j, D, e, −t, −t, e, D, j, −o, −y, 0, y, o, −j, −D, −e, t,} { A, k, −p,−v, e, F, f, −u, −q, j, B, a, −z, −l, o, w, −d, −E, −g, t, r, −i, −C,−b, y, m, −n, −x, c, D, h, −s,} { C, g, −v, −n, o, u, −h, −B, a, D, f,−w, −m, p, t, −i, −A, b, E, e, −x, −l, q, s, −j, −z, c, F, d, −y, −k,r,} { E, c, −B, −f, y, i, −v, −l, s, o, −p, −r, m, u, −j, −x, g, A, −d,−D, a, F, b, −C, −e, z, h, −w, −k, t, n, −q,} { F, −a, −E, b, D, −c, −C,d, B, −e, −A, f, z, −g, −y, h, x, −i, −w, j, v, −k, −u, l, t, −m, −s, n,r, −o, −q, p,} { D, −e, −y, j, t, −o, −o, t, j, −y, −e, D, 0, −D, e, y,−j, −t, o, o, −t, −j, y, e, −D, 0, D, −e, −y, j, t, −o,} { B, −i, −s, r,j, −A, −a, C, −h, −t, q, k, −z, −b, D, −g, −u, p, l, −y, −c, E, −f, −v,o, m, −x, −d, F, −e, −w, n,} { z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m,−m, z, 0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m,} {x, −q, −g, E, −j, −n, A, −c, −u, t, d, −B, m, k, −D, f, r, −w, −a, y,−p, −h, F, −i, −o, z, −b, −v, s, e, −C, l,} { v, −u, −a, w, −t, −b, x,−s, −c, y, −r, −d, z, −q, −e, A, −p, −f, B, −o, −g, C, −n, −h, D, −m,−i, E, −l, −j, F, −k,} { t, −y, e, o, −D, j, j, −D, o, e, −y, t, 0, −t,y, −e, −o, D, −j, −j, D, −o, −e, y, −t, 0, t, −y, e, o, −D, j,} { r, −C,k, g, −y, v, −d, −n, F, −o, −c, u, −z, h, j, −B, s, −a, −q, D, −l, −f,x, −w, e, m, −E, p, b, −t, A, −i,} { p, −F, q, −a, −o, E, −r, b, n, −D,s, −c, −m, C, −t, d, l, −B, u, −e, −k, A, −v, f, j, −z, w, −g, −i, y,−x, h,} { n, −B, w, −i, −e, s, −F, r, −d, −j, x, −A, m, a, −o, C, −v, h,f, −t, E, −q, c, k, −y, z, −l, −b, p, −D, u, −g,} { l, −x, C, −q, e, g,−s, E, −v, j, b, −n, z, −A, o, −c, −i, u, −F, t, −h, −d, p, −B, y, −m,a, k, −w, D, −r, f,} { j, −t, D, −y, o, −e, −e, o, −y, D, −t, j, 0, −j,t, −D, y, −o, e, e, −o, y, −D, t, −j, 0, j, −t, D, −y, o, −e,} { h, −p,x, −F, y, −q, i, −a, −g, o, −w, E, −z, r, −j, b, f, −n, v, −D, A, −s, k,−c, −e, m, −u, C, −B, t, −l, d,} { f, −l, r, −x, D, −C, w, −q, k, −e,−a, g, −m, s, −y, E, −B, v, −p, j, −d, −b, h, −n, t, −z, F, −A, u, −o,i, −c,} { d, −h, l, −p, t, −x, B, −F, C, −y, u, −q, m, −i, e, −a, −c, g,−k, o, −s, w, −A, E, −D, z, −v, r, −n, j, −f, b,} { b, −d, f, −h, j, −l,n, −p, r, −t, v, −x, z, −B, D, −F, E, −C, A, −y, w, −u, s, −q, o, −m, k,−i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u,v, w, x, y, z, A, B, C, D, E, F}={4, 9, 13, 17, 21, 26, 30, 34, 38, 42,46, 50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 87,88, 89, 90, 90}, and wherein the second transform core matrix is a32-point DCT-8 that is constructed using following matrix: { a, b, c, d,e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B,C, D, E, F,} { b, e, h, k, n, q, t, w, z, C, F, −E, −B, −y, −v, −s, −p,−m, −j, −g, −d, −a, −c, −f, −i, −l, −o, −r, −u, −x, −A, −D,} { c, h, m,r, w, B, 0, −B, −w, −r, −m, −h, −c, −c, −h, −m, −r, −w, −B, 0, B, w, r,m, h, c, c, h, m, r, w, B,} { d, k, r, y, F, −A, −t, −m, −f, −b, −i, −p,−w, −D, C, v, o, h, a, g, n, u, B, −E, −x, −q, −j, −c, −e, −l, −s, −z,}{ e, n, w, F, −y, −p, −g, −c, −l, −u, −D, A, r, i, a, j, s, B, −C, −t,−k, −b, −h, −q, −z, E, v, m, d, f, o, x,} { f, q, B, −A, −p, −e, −g, −r,−C, z, o, d, h, s, D, −y, −n, −c, −i, −t, −E, x, m, b, j, u, F, −w, −l,−a, −k, −v,} { g, t, 0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g,−t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t,} { h, w, −B, −m,−c, −r, 0, r, c, m, B, −w, −h, −h, −w, B, m, c, r, 0, −r, −c, −m, −B, w,h, h, w, −B, −m, −c, −r,} { i, z, −w, −f, −l, −C, t, c, o, F, −q, −a,−r, E, n, d, u, −B, −k, −g, −x, y, h, j, A, −v, −e, −m, −D, s, b, p,} {j, C, −r, −b, −u, z, g, m, F, −o, −e, −x, w, d, p, −E, −l, −h, −A, t, a,s, −B, −i, −k, −D, q, c, v, −y, −f, −n,} { k, F, −m, −i, −D, o, g, B,−q, −e, −z, s, c, x, −u, −a, −v, w, b, t, −y, −d, −r, A, f, p, −C, −h,−n, E, j, l,} { l, −E, −h, −p, A, d, t, −w, −a, −x, s, e, B, −o, −i, −F,k, m, −D, −g, −q, z, c, u, −v, −b, −y, r, f, C, −n, −j,} { m, −B, −c,−w, r, h, 0, −h, −r, w, c, B, −m, −m, B, c, w, −r, −h, 0, h, r, −w, −c,−B, m, m, −B, −c, −w, r, h,} { n, −y, −c, −D, i, s, −t, −h, E, d, x, −o,−m, z, b, C, −j, −r, u, g, −F, −e, −w, p, l, −A, −a, −B, k, q, −v, −f,}{ o, −v, −h, C, a, D, −g, −w, n, p, −u, −i, B, b, E, −f, −x, m, q, −t,−j, A, c, F, −e, −y, l, r, −s, −k, z, d,} { p, −s, −m, v, j, −y, −g, B,d, −E, −a, −F, c, C, −f, −z, i, w, −l, −t, o, q, −r, −n, u, k, −x, −h,A, e, −D, −b,} { q, −p, −r, o, s, −n, −t, m, u, −l, −v, k, w, −j, −x, i,y, −h, −z, g, A, −f, −B, e, C, −d, −D, c, E, −b, −F, a,} { r, −m, −w, h,B, −c, 0, c, −B, −h, w, m, −r, −r, m, w, −h, −B, c, 0, −c, B, h, −w, −m,r, r, −m, −w, h, B, −c,} { s, −j, −B, a, −C, −i, t, r, −k, −A, b, −D,−h, u, q, −l, −z, c, −E, −g, v, p, −m, −y, d, −F, −f, w, o, −n, −x, e,}{ t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t, t,−g, 0, g, −t, −t, g, 0, −g, t, t, −g,} { u, −d, B, n, −k, −E, g, −r, −x,a, −y, −q, h, −F, −j, o, A, −c, v, t, −e, C, m, −l, −D, f, −s, −w, b,−z, −p, i,} { v, −a, w, u, −b, x, t, −c, y, s, −d, z, r, −e, A, q, −f,B, p, −g, C, o, −h, D, n, −i, E, m, −j, F, l, −k,} { w, −c, r, B, −h, m,0, −m, h, −B, −r, c, −w, −w, c, −r, −B, h, −m, 0, m, −h, B, r, −c, w, w,−c, r, B, −h, m,} { x, −f, m, −E, −q, b, −t, −B, j, −i, A, u, −c, p, F,−n, e, −w, −y, g, −l, D, r, −a, s, C, −k, h, −z, −v, d, −o,} { y, −i, h,−x, −z, j, −g, w, A, −k, f, −v, −B, l, −e, u, C, −m, d, −t, −D, n, −c,s, E, −o, b, −r, −F, p, −a, q,} { z, −l, c, −q, E, u, −g, h, −v, −D, p,−b, m, −A, −y, k, −d, r, −F, −t, f, −i, w, C, −o, a, −n, B, x, −j, e,−s,} { A, −o, c, −j, v, F, −t, h, −e, q, −C, −y, m, −a, l, −x, −D, r,−f, g, −s, E, w, −k, b, −n, z, B, −p, d, −i, u,} { B, −r, h, −c, m, −w,0, w, −m, c, −h, r, −B, −B, r, −h, c, −m, w, 0, −w, m, −c, h, −r, B, B,−r, h, −c, m, −w,} { C, −u, m, −e, d, −l, t, −B, −D, v, −n, f, −c, k,−s, A, E, −w, o, −g, b, −j, r, −z, −F, x, −p, h, −a, i, −q, y,} { D, −x,r, −l, f, −a, g, −m, s, −y, E, C, −w, q, −k, e, −b, h, −n, t, −z, F, B,−v, p, −j, d, −c, i, −o, u, −A,} { E, −A, w, −s, o, −k, g, −c, b, −f, j,−n, r, −v, z, −D, −F, B, −x, t, −p, l, −h, d, −a, e, −i, m, −q, u, −y,C,} { F, −D, B, −z, x, −v, t, −r, p, −n, l, −j, h, −f, d, −b, a, −c, e,−g, i, −k, m, −o, q, −s, u, −w, y, −A, C, −E,},

wherein{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u,v, w, x, y, z, A, B, C, D, E, F}={90, 90, 89, 88, 87, 86, 85, 84, 82,80, 78, 77, 74, 72, 68, 66, 63, 60, 56, 53, 50, 46, 42, 38, 34, 30, 26,21, 17, 13, 9, 4}.
 10. The apparatus of claim 8, wherein the secondtransform core matrix is a 16-point DCT-8 that is constructed usingfollowing matrix:   { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,} {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,} { c, h, m,−p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, l,} { d, k, −p, −i, −b, −f,−m, n, g, a, h, o, −l, −e, −c, −j,} { e, n, −k, −b, −h, 0, h, b, k, −n,−e, −e, −n, k, b, h,} { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0,−f, −f,} { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d,} {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,} { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} { j, −e, −o, a, −n, −f, i, k,−d, −p, b, −m, −g, h, l, −c,} { k, −b, n, h, −e, 0, e, −h, −n, b, −k,−k, b, −n, −h, e,} { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n,d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,} { n,−h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,} { o, −k, g, −c, b,−f, j, −n, −p, l, −h, d, −a, e, −i, m,} { p, −n, l, −j, h, −f, d, −b, a,−c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 86,86, 81, 77, 74, 68, 61, 54, 48, 40, 34, 25, 18, 7}.
 11. The apparatus ofclaim 8, wherein the first transform core matrix is a 16-point DST-7that is constructed using following matrix:   { a, b, c, d, e, f, g, h,i, j, k, l, m, n, o, p,} { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i,−l, −o,} { e, j, o, m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g,n, l, e, −b, −i, −p, −j, −c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l,−l, −c, f, o, i, 0, −i, −o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0,−k, −k, 0, k, k, 0, −k,} { m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d,−p, −c, j,} { o, c, −l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} {p, −a, −o, b, n, −c, −m, d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j,d, −o, a, m, −f, −h, k, c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c,−i, l, 0, −l, i, c, −o, f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l,−b, −h, o, −e,} { h, −p, i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l,d,} { f, −l, o, −i, c, c, −i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h,l, −p, m, −i, e, −a, −c, g, −k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l,n, −p, o, −m, k, −i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={9, 17, 25, 33,41, 48, 55, 61, 68, 72, 77, 81, 85, 86, 88, 89}, and wherein the secondtransform core matrix is a 16-point DCT-8 that is constructed usingfollowing matrix:   { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,} {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,} { c, h, m,−p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, l,} { d, k, −p, −i, −b, −f,−m, n, g, a, h, o, −l, −e, −c, −j,} { e, n, −k, −b, −h, 0, h, b, k, −n,−e, −e, −n, k, b, h,} { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0,−f, −f,} { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d,} {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,} { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} { j, −e, −o, a, −n, −f, i, k,−d, −p, b, −m, −g, h, l, −c,} { k, −b, n, h, −e, 0, e, −h, −n, b, −k,−k, b, −n, −h, e,} { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n,d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,} { n,−h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,} { o, −k, g, −c, b,−f, j, −n, −p, l, −h, d, −a, e, −i, m,} { p, −n, l, −j, h, −f, d, −b, a,−c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={89, 88, 86,85, 81, 77, 72, 68, 61, 55, 48, 41, 33, 25, 17, 9}.
 12. The apparatus ofclaim 8, wherein the first transform core matrix is a 16-point DST-7that is constructed using following matrix:   { a, b, c, d, e, f, g, h,i, j, k, l, m, n, o, p,} { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i,−l, −o,} { e, j, o, m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g,n, l, e, −b, −i, −p, −j, −c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l,−l, −c, f, o, i, 0, −i, −o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0,−k, −k, 0, k, k, 0, −k,} { m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d,−p, −c, j,} { o, c, −l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} {p, −a, −o, b, n, −c, −m, d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j,d, −o, a, m, −f, −h, k, c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c,−i, l, 0, −l, i, c, −o, f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l,−b, −h, o, −e,} { h, −p, i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l,d,} { f, −l, o, −i, c, c, −i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h,l, −p, m, −i, e, −a, −c, g, −k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l,n, −p, o, −m, k, −i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={8, 17, 25, 33,40, 48, 55, 62, 68, 73, 77, 81, 85, 87, 88, 88}, and wherein the secondtransform core matrix is a 16-point DCT-8 that is constructed usingfollowing matrix:   { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,} {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,} { c, h, m,−p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, l,} { d, k, −p, −i, −b, −f,−m, n, g, a, h, o, −l, −e, −c, −j,} { e, n, −k, −b, −h, 0, h, b, k, −n,−e, −e, −n, k, b, h,} { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0,−f, −f,} { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d,} {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,} { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} { j, −e, −o, a, −n, −f, i, k,−d, −p, b, −m, −g, h, l, −c,} { k, −b, n, h, −e, 0, e, −h, −n, b, −k,−k, b, −n, −h, e,} { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n,d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,} { n,−h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,} { o, −k, g, −c, b,−f, j, −n, −p, l, −h, d, −a, e, −i, m,} { p, −n, l, −j, h, −f, d, −b, a,−c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 87,85, 81, 77, 73, 68, 62, 55, 48, 40, 33, 25, 17, 8}.
 13. The apparatus ofclaim 8, wherein the control information comprises at least one of:Supplementary Enhancement Information (SEI) messages and Video UsabilityInformation (VUI) parameter set fragments.
 14. A non-transitorycomputer-readable storage medium storing instructions that cause atleast one processor to: receive information regarding a video sequencefor decoding, wherein the video sequence information comprises one ormore symbols corresponding to control information to manage operation ofone or more devices, the control information comprising memory addressesof prediction samples corresponding to a reference picture associatedwith the video sequence, the prediction samples being configured to becontrolled by motion vectors; determine, for the decoding of the videosequence, whether to use a first transform core matrix that is of afirst size type or a second transform core matrix that is of a secondsize type, wherein the first transform core matrix is one of a 16 pointdiscrete sine transform (DST)-7 or a 32 point DST-7, wherein the secondtransform core matrix is one of a 16 point discrete cosine transform(DCT)-8 or a 32 point DCT-8, and wherein the 16-point DST-7 isconstructed using following matrix:   { a, b, c, d, e, f, g, h, i, j, k,l, m, n, o, p,} { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o,}{ e, j, o, m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g, n, l, e,−b, −i, −p, −j, −c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l, −l, −c,f, o, i, 0, −i, −o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0,k, k, 0, −k,} { m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c,j,} { o, c, −l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} { p, −a,−o, b, n, −c, −m, d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j, d, −o,a, m, −f, −h, k, c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c, −i, l,0, −l, i, c, −o, f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l, −b, −h,o, −e,} { h, −p, i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l, d,} { f,−l, o, −i, c, c, −i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h, l, −p, m,−i, e, −a, −c, g, −k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l, n, −p, o,−m, k, −i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={7, 18, 25, 34,40, 48, 54, 61, 68, 74, 77, 81, 86, 86, 88, 88}; and based on thedetermining, transmit information that causes the video sequence to bedecoded by the one or more devices using the determined first transformcore matrix or second transform core matrix.
 15. The non-transitorycomputer-readable storage medium of claim 14, wherein the determining ofwhether to use the first transform core matrix that is of the first sizetype or the second transform core matrix this is of the second size typeis based on a flag signaled using two bins to identify a horizontaltransform and a vertical transform.
 16. The non-transitorycomputer-readable storage medium of claim 14, wherein the firsttransform core matrix is a 32-point DST-7 that is constructed using thefollowing matrix: { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q,r, s, t, u, v, w, x, y, z, A, B, C, D, E, F,} { c, f, i, l, o, r, u, x,A, D, F, C, z, w, t, q, n, k, h, e, b, −a, −d, −g, −j, −m, −p, −s, −v,−y, −B, −E,} { e, j, o, t, y, D, D, y, t, o, j, e, 0, −e, −j, −o, −t,−y, −D, −D, −y, −t, −o, −j, −e, 0, e, j, o, t, y, D,} { g, n, u, B, D,w, p, i, b, −e, −l, −s, −z, −F, −y, −r, −k, −d, c, j, q, x, E, A, t, m,f, −a, −h, −o, −v, −C,} { i, r, A, C, t, k, b, −g, −p, −y, −E, −v, −m,−d, e, n, w, F, x, o, f, −c, −l, −u, −D, −z, −q, −h, a, j, s, B,} { k,v, F, u, j, −a, −l, −w, −E, −t, −i, b, m, x, D, s, h, −c, −n, −y, −C,−r, −g, d, o, z, B, q, f, −e, −p, −A,} { m, z, z, m, 0, −m, −z, −z, −m,0, m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0,m, z,} { o, D, t, e, −j, −y, −y, −j, e, t, D, o, 0, −o, −D, −t, −e, j,y, y, j, −e, −t, −D, −o, 0, o, D, t, e, −j, −y,} { q, E, n, −c, −t, −B,−k, f, w, y, h, −i, −z, −v, −e, l, C, s, b, −o, −F, −p, a, r, D, m, −d,−u, −A, −j, g, x,} { s, A, h, −k, −D, −p, c, v, x, e, −n, −F, −m, f, y,u, b, −q, −C, −j, i, B, r, −a, −t, −z, −g, l, E, o, −d, −w,} { u, w, b,−s, −y, −d, q, A, f, −o, −C, −h, m, E, j, −k, −F, −l, i, D, n, −g, −B,−p, e, z, r, −c, −x, −t, a, v,} { w, s, −d, −A, −o, h, E, k, −l, −D, −g,p, z, c, −t, −v, a, x, r, −e, −B, −n, i, F, j, −m, −C, −f, q, y, b, −u,}{ y, o, −j, −D, −e, t, t, −e, −D, −j, o, y, 0, −y, −o, j, D, e, −t, −t,e, D, j, −o, −y, 0, y, o, −j, −D, −e, t,} { A, k, −p, −v, e, F, f, −u,−q, j, B, a, −z, −l, o, w, −d, −E, −g, t, r, −i, −C, −b, y, m, −n, −x,c, D, h, −s,} { C, g, −v, −n, o, u, −h, −B, a, D, f, −w, −m, p, t, −i,−A, b, E, e, −x, −l, q, s, −j, −z, c, F, d, −y, −k, r,} { E, c, −B, −f,y, i, −v, −l, s, o, −p, −r, m, u, −j, −x, g, A, −d, −D, a, F, b, −C, −e,z, h, −w, −k, t, n, −q,} { F, −a, −E, b, D, −c, −C, d, B, −e, −A, f, z,−g, −y, h, x, −i, −w, j, v, −k, −u, l, t, −m, −s, n, r, −o, −q, p,} { D,−e, −y, j, t, −o, −o, t, j, −y, −e, D, 0, −D, e, y, −j, −t, o, o, −t,−j, y, e, −D, 0, D, −e, −y, j, t, −o,} { B, −i, −s, r, j, −A, −a, C, −h,−t, q, k, −z, −b, D, −g, −u, p, l, −y, −c, E, −f, −v, o, m, −x, −d, F,−e, −w, n,} { z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m,m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m,} { x, −q, −g, E, −j,−n, A, −c, −u, t, d, −B, m, k, −D, f, r, −w, −a, y, −p, −h, F, −i, −o,z, −b, −v, s, e, −C, l,} { v, −u, −a, w, −t, −b, x, −s, −c, y, −r, −d,z, −q, −e, A, −p, −f, B, −o, −g, C, −n, −h, D, −m, −i, E, −l, −j, F,−k,} { t, −y, e, o, −D, j, j, −D, o, e, −y, t, 0, −t, y, −e, −o, D, −j,−j, D, −o, −e, y, −t, 0, t, −y, e, o, −D, j,} { r, −C, k, g, −y, v, −d,−n, F, −o, −c, u, −z, h, j, −B, s, −a, −q, D, −l, −f, x, −w, e, m, −E,p, b, −t, A, −i,} { p, −F, q, −a, −o, E, −r, b, n, −D, s, −c, −m, C, −t,d, l, −B, u, −e, −k, A, −v, f, j, −z, w, −g, −i, y, −x, h,} { n, −B, w,−i, −e, s, −F, r, −d, −j, x, −A, m, a, −o, C, −v, h, f, −t, E, −q, c, k,−y, z, −l, −b, p, −D, u, −g,} { l, −x, C, −q, e, g, −s, E, −v, j, b, −n,z, −A, o, −c, −i, u, −F, t, −h, −d, p, −B, y, −m, a, k, −w, D, −r, f,} {j, −t, D, −y, o, −e, −e, o, −y, D, −t, j, 0, −j, t, −D, y, −o, e, e, −o,y, −D, t, −j, 0, j, −t, D, −y, o, −e,} { h, −p, x, −F, y, −q, i, −a, −g,o, −w, E, −z, r, −j, b, f, −n, v, −D, A, −s, k, −c, −e, m, −u, C, −B, t,−l, d,} { f, −l, r, −x, D, −C, w, −q, k, −e, −a, g, −m, s, −y, E, −B, v,−p, j, −d, −b, h, −n, t, −z, F, −A, u, −o, i, −c,} { d, −h, l, −p, t,−x, B, −F, C, −y, u, −q, m, −i, e, −a, −c, g, −k, o, −s, w, −A, E, −D,z, −v, r, −n, j, −f, b,} { b, −d, f, −h, j, −l, n, −p, r, −t, v, −x, z,−B, D, −F, E, −C, A, −y, w, −u, s, −q, o, −m, k, −i, g, −e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u,v, w, x, y, z, A, B, C, D, E, F}={4, 9, 13, 17, 21, 26, 30, 34, 38, 42,46, 50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 87,88, 89, 90, 90}, and wherein the second transform core matrix is a32-point DCT-8 that is constructed using following matrix: { a, b, c, d,e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B,C, D, E, F,} { b, e, h, k, n, q, t, w, z, C, F, −E, −B, −y, −v, −s, −p,−m, −j, −g, −d, −a, −c, −f, −i, −l, −o, −r, −u, −x, −A, −D,} { c, h, m,r, w, B, 0, −B, −w, −r, −m, −h, −c, −c, −h, −m, −r, −w, −B, 0, B, w, r,m, h, c, c, h, m, r, w, B,} { d, k, r, y, F, −A, −t, −m, −f, −b, −i, −p,−w, −D, C, v, o, h, a, g, n, u, B, −E, −x, −q, −j, −c, −e, −l, −s, −z,}{ e, n, w, F, −y, −p, −g, −c, −l, −u, −D, A, r, i, a, j, s, B, −C, −t,−k, −b, −h, −q, −z, E, v, m, d, f, o, x,} { f, q, B, −A, −p, −e, −g, −r,−C, z, o, d, h, s, D, −y, −n, −c, −i, −t, −E, x, m, b, j, u, F, −w, −l,−a, −k, −v,} { g, t, 0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g,−t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t,} { h, w, −B, −m,−c, −r, 0, r, c, m, B, −w, −h, −h, −w, B, m, c, r, 0, −r, −c, −m, −B, w,h, h, w, −B, −m, −c, −r,} { i, z, −w, −f, −l, −C, t, c, o, F, −q, −a,−r, E, n, d, u, −B, −k, −g, −x, y, h, j, A, −v, −e, −m, −D, s, b, p,} {j, C, −r, −b, −u, z, g, m, F, −o, −e, −x, w, d, p, −E, −l, −h, −A, t, a,s, −B, −i, −k, −D, q, c, v, −y, −f, −n,} { k, F, −m, −i, −D, o, g, B,−q, −e, −z, s, c, x, −u, −a, −v, w, b, t, −y, −d, −r, A, f, p, −C, −h,−n, E, j, l,} { l, −E, −h, −p, A, d, t, −w, −a, −x, s, e, B, −o, −i, −F,k, m, −D, −g, −q, z, c, u, −v, −b, −y, r, f, C, −n, −j,} { m, −B, −c,−w, r, h, 0, −h, −r, w, c, B, −m, −m, B, c, w, −r, −h, 0, h, r, −w, −c,−B, m, m, −B, −c, −w, r, h,} { n, −y, −c, −D, i, s, −t, −h, E, d, x, −o,−m, z, b, C, −j, −r, u, g, −F, −e, −w, p, l, −A, −a, −B, k, q, −v, −f,}{ o, −v, −h, C, a, D, −g, −w, n, p, −u, −i, B, b, E, −f, −x, m, q, −t,−j, A, c, F, −e, −y, l, r, −s, −k, z, d,} { p, −s, −m, v, j, −y, −g, B,d, −E, −a, −F, c, C, −f, −z, i, w, −l, −t, o, q, −r, −n, u, k, −x, −h,A, e, −D, −b,} { q, −p, −r, o, s, −n, −t, m, u, −l, −v, k, w, −j, −x, i,y, −h, −z, g, A, −f, −B, e, C, −d, −D, c, E, −b, −F, a,} { r, −m, −w, h,B, −c, 0, c, −B, −h, w, m, −r, −r, m, w, −h, −B, c, 0, −c, B, h, −w, −m,r, r, −m, −w, h, B, −c,} { s, −j, −B, a, −C, −i, t, r, −k, −A, b, −D,−h, u, q, −l, −z, c, −E, −g, v, p, −m, −y, d, −F, −f, w, o, −n, −x, e,}{ t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t, t,−g, 0, g, −t, −t, g, 0, −g, t, t, −g,} { u, −d, B, n, −k, −E, g, −r, −x,a, −y, −q, h, −F, −j, o, A, −c, v, t, −e, C, m, −l, −D, f, −s, −w, b,−z, −p, i,} { v, −a, w, u, −b, x, t, −c, y, s, −d, z, r, −e, A, q, −f,B, p, −g, C, o, −h, D, n, −i, E, m, −j, F, l, −k,} { w, −c, r, B, −h, m,0, −m, h, −B, −r, c, −w, −w, c, −r, −B, h, −m, 0, m, −h, B, r, −c, w, w,−c, r, B, −h, m,} { x, −f, m, −E, −q, b, −t, −B, j, −i, A, u, −c, p, F,−n, e, −w, −y, g, −l, D, r, −a, s, C, −k, h, −z, −v, d, −o,} { y, −i, h,−x, −z, j, −g, w, A, −k, f, −v, −B, l, −e, u, C, −m, d, −t, −D, n, −c,s, E, −o, b, −r, −F, p, −a, q,} { z, −l, c, −q, E, u, −g, h, −v, −D, p,−b, m, −A, −y, k, −d, r, −F, −t, f, −i, w, C, −o, a, −n, B, x, −j, e,−s,} { A, −o, c, −j, v, F, −t, h, −e, q, −C, −y, m, −a, l, −x, −D, r,−f, g, −s, E, w, −k, b, −n, z, B, −p, d, −i, u,} { B, −r, h, −c, m, −w,0, w, −m, c, −h, r, −B, −B, r, −h, c, −m, w, 0, −w, m, −c, h, −r, B, B,−r, h, −c, m, −w,} { C, −u, m, −e, d, −l, t, −B, −D, v, −n, f, −c, k,−s, A, E, −w, o, −g, b, −j, r, −z, −F, x, −p, h, −a, i, −q, y,} { D, −x,r, −l, f, −a, g, −m, s, −y, E, C, −w, q, −k, e, −b, h, −n, t, −z, F, B,−v, p, −j, d, −c, i, −o, u, −A,} { E, −A, w, −s, o, −k, g, −c, b, −f, j,−n, r, −v, z, −D, −F, B, −x, t, −p, l, −h, d, −a, e, −i, m, −q, u, −y,C,} { F, −D, B, −z, x, −v, t, −r, p, −n, l, −j, h, −f, d, −b, a, −c, e,−g, i, −k, m, −o, q, −s, u, −w, y, −A, C, −E,},

wherein{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u,v, w, x, y, z, A, B, C, D, E, F}={90, 90, 89, 88, 87, 86, 85, 84, 82,80, 78, 77, 74, 72, 68, 66, 63, 60, 56, 53, 50, 46, 42, 38, 34, 30, 26,21, 17, 13, 9, 4}.
 17. The non-transitory computer-readable storagemedium of claim 14, wherein the second transform core matrix is a16-point DCT-8 that is constructed using following matrix: { a, b, c, d,e, f, g, h, i, j, k, 1, m, n, o, p,} { b, e, h, k, n, 0, −n, −k, −h, −e,−b, −b, −e, −h, −k, −n,} { c, h, m, −p, −k, −f, −a, −e, −j, −o, n, i, d,b, g, l,} { d, k, −p, −i, −b, −f, −m, n, g, a, h, o, −l, −e, −c, −j,} {e, n, −k, −b, −h, 0, h, b, k, −n, −e, −e, −n, k, b, h,} { f, 0, −f, −f,0, f, f, 0, −f, −f, 0, f, f, 0, −f, −f,} { g, −n, −a, −m, h, f, −o, −b,−l, i, e, −p, −c, −k, j, d,} { h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h,k, e, −n, −b,} { i, −h, −j, g, k, −f, −l, e, m, −d, −n, c, o, −b, −p,a,} { j, −e, −o, a, −n, −f, i, k, −d, −p, b, −m, −g, h, l, −c,} { k, −b,n, h, −e, 0, e, −h, −n, b, −k, −k, b, −n, −h, e,} { l, −b, i, o, −e, f,−p, −h, c, −m, −k, a, −j, −n, d, −g, } { m, −e, d, −l, −n, f, −c, k, o,−g, b, −j, −p, h, −a, i,} { n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h,−b, e, −k,} { o, −k, g, −c, b, −f, j, −n, −p, l, −h, d, −a, e, −i, m,} {p, −n, l, −j, h, −f, d, −b, a, −c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 86,86, 81, 77, 74, 68, 61, 54, 48, 40, 34, 25, 18, 7}.
 18. Thenon-transitory computer-readable storage medium of claim 14, wherein thefirst transform core matrix is a 16-point DST-7 that is constructedusing following matrix:   { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o,p,} { c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o,} { e, j, o,m, h, c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g, n, l, e, −b, −i, −p,−j, −c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l, −l, −c, f, o, i, 0,−i, −o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k, k, 0,−k,} { m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c, j,} { o, c,−l, −f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} { p, −a, −o, b, n, −c,−m, d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j, d, −o, a, m, −f, −h,k, c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c, −i, l, 0, −l, i, c,−o, f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l, −b, −h, o, −e,} { h,−p, i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l, d,} { f, −l, o, −i, c,c, −i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h, l, −p, m, −i, e, −a, −c,g, −k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l, n, −p, o, −m, k, −i, g,−e, c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={9, 17, 25, 33,41, 48, 55, 61, 68, 72, 77, 81, 85, 86, 88, 89}, and wherein the secondtransform core matrix is a 16-point DCT-8 that is constructed usingfollowing matrix: { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, } {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,} { c, h, m,−p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, l,} { d, k, −p, −i, −b, −f,−m, n, g, a, h, o, −l, −e, −c, −j,} { e, n, −k, −b, −h, 0, h, b, k, −n,−e, −e, −n, k, b, h,} { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0,−f, −f,} { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d,} {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,} { i, −h, −j, g,k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} { j, −e, −o, a, −n, −f, i, k,−d, −p, b, −m, −g, h, l, −c,} { k, −b, n, h, −e, 0, e, −h, −n, b, −k,−k, b, −n, −h, e,} { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j, −n,d, −g,} { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,} { n,−h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,} { o, −k, g, −c, b,−f, j, −n, −p, l, −h, d, −a, e, −i, m,} { p, −n, l, −j, h, −f, d, −b, a,−c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, j, k, l, m, n, o, p}={89, 88, 86, 85,81, 77, 72, 68, 61, 55, 48, 41, 33, 25, 17, 9}.
 19. The non-transitorycomputer-readable storage medium of claim 14, wherein the firsttransform core matrix is a 16-point DST-7 that is constructed usingfollowing matrix: { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,} {c, f, i, l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o,} { e, j, o, m, h,c, −b, −g, −l, −p, −k, −f, −a, d, i, n,} { g, n, l, e, −b, −i, −p, −j,−c, d, k, o, h, a, −f, −m,} { i, o, f, −c, −l, −l, −c, f, o, i, 0, −i,−o, −f, c, l,} { k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k, k, 0, −k,} {m, g, −f, −n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c, j,} { o, c, −l,−f, i, i, −f, −l, c, o, 0, −o, −c, l, f, −i,} { p, −a, −o, b, n, −c, −m,d, l, −e, −k, f, j, −g, −i, h,} { n, −e, −i, j, d, −o, a, m, −f, −h, k,c, −p, b, l, −g,} { l, −i, −c, o, −f, −f, o, −c, −i, l, 0, −l, i, c, −o,f,} { j, −m, c, g, −p, f, d, −n, i, a, −k, l, −b, −h, o, −e,} { h, −p,i, −a, −g, o, −j, b, f, −n, k, −c, −e, m, −l, d,} { f, −l, o, −i, c, c,−i, o, −l, f, 0, −f, l, −o, i, −c,} { d, −h, l, −p, m, −i, e, −a, −c, g,−k, o, −n, j, −f, b,} { b, −d, f, −h, j, −l, n, −p, o, −m, k, −i, g, −e,c, −a,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={8, 17, 25, 33,40, 48, 55, 62, 68, 73, 77, 81, 85, 87, 88, 88}, and wherein the secondtransform core matrix is a 16-point DCT-8 that is constructed usingfollowing matrix: { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,}  {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b, −e, −h, −k, −n,}  { c, h, m,−p, −k, −f, −a, −e, −j, −o, n, i, d, b, g, l,}  { d, k, −p, −i, −b, −f,−m, n, g, a, h, o, −l, −e, −c, −j,}  { e, n, −k, −b, −h, 0, h, b, k, −n,−e, −e, −n, k, b, h,}  { f, 0, −f, −f, 0, f, f, 0, −f, −f, 0, f, f, 0,−f, −f,}  { g, −n, −a, −m, h, f, −o, −b, −l, i, e, −p, −c, −k, j, d,}  {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e, −n, −b,}  { i, −h, −j,g, k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,}  { j, −e, −o, a, −n, −f,i, k, −d, −p, b, −m, −g, h, l, −c,}  { k, −b, n, h, −e, 0, e, −h, −n, b,−k, −k, b, −n, −h, e,}  { l, −b, i, o, −e, f, −p, −h, c, −m, −k, a, −j,−n, d, −g,}  { m, −e, d, −l, −n, f, −c, k, o, −g, b, −j, −p, h, −a, i,} { n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,}  { o, −k, g,−c, b, −f, j, −n, −p, l, −h, d, −a, e, −i, m,}  { p, −n, l, −j, h, −f,d, −b, a, −c, e, −g, i, −k, m, −o,},

wherein {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}={88, 88, 87,85, 81, 77, 73, 68, 62, 55, 48, 40, 33, 25, 17, 8}.
 20. Thenon-transitory computer-readable storage medium of claim 14, wherein thecontrol information comprises at least one of: Supplementary EnhancementInformation (SEI) messages and Video Usability Information (VUI)parameter set fragments.